Ncert -class 10-Maths- Introduction to Trigonometry Welcome to your Ncert -class 10-Maths- Introduction to Trigonometry 1. Assertion(A):- If x = a cos 0 and y = b sin 0, then b²x² + a²y² = a²b².Reason(R)- b²x² + a²y² = a²b² where x = a and y = 0. Assertion (A) is true but reason (R) is false. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). Assertion (A) is false but reason (R) is true. None 2. If cos(α + β ) = 0, then the value of sin( α - β )is sin α sin 2α cos 2β cos β None 3. In the right triangle PQR, PR=5cm, PQ=4cm, RQ=3cm then the value of secRis: 3/5 5/3 3/4 4/3 None 4. Assertion: The value of tanA = 1 for all values of A.Reason: tan 45º = 1. Assertion (A) is true but reason (R) is false. Assertion (A) is false but reason (R) is true. . Both assertion (A) and reason (R) are true but reason(R) is not the correct explanation of assertion (A). Both assertion (A) and reason (R) are true and reason(R) is the correct explanation of assertion (A). None 5. If two tangents inclined at an angle 60º are drawn to a circle of radius 3 cm, thenthe length of each tangent is 32 √3 cm 3cm 3√3 cm 6cm None 6. Assertion : sin² 67º + cos² 67º = 1Reanson : For any value of θ ,sin² θ +cos² θ =1 Assertion (A) is true but reason (R) is false. Assertion (A) is false but reason (R) is true. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). None 7. Assertion : The value of sin θ = 4/3 is not possible. Reanson : Hypotenuse is the largest side in any right angled triangle. Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). Assertion (A) is true but reason (R) is false. Assertion (A) is false but reason (R) is true Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). None 8. Assertion:- The value of cos60º cosec30º– cot60º cot30º is 0Reason- complementary relations are cosθ=sin (90º- θ), cosecθ = sec (90º- θ), cotθ = tan(90º- θ). Assertion (A) is false but reason (R) is true. Assertion (A) is true but reason (R) is false. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). None 9. None 10. The value of θ, for which tan²θ = √3 is: 15 90 45 30 None 11. In a right triangle PQR, right-angled at Q, if cotR = 1 then the value of2cosecRsecR is: 1 4 2√2 2 None 12. Assertion:- For the value of θ = 60º, for sin 2θ = 1,where 0º < θ < 90ºReason- for any angle (θ), sin²θ + cos²θ =1. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) Assertion (A) is false but reason (R) is true Assertion (A) is true but reason (R) is false None 13. If A and B are acute angles and sin A = cos B, then find the value of (A + B) . 60º 30º 90º 40º None 14. If sinӨ – cosӨ = 0, then the value of \(sin^{4}\theta + cos^{4}\theta \)is 1/4 1 1/2 3/4 None 15. Assertion : If x sin³θ + y cos³θ = sinθ cosθ and x sinθ = y cosθ, then x²+ y² = 1Reason : For any value of θ, sin²θ + cos²θ = 1. Assertion (A) is true but reason (R) is false. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). Assertion (A) is false but reason (R) is true. None 16. In triangle XYZ right angled at Y, XY = √3 cm and XZ = 2 cm then the ratiobetween angle XZY and ZXY is: 2 : 3 2: 1 1: 2 3: 4 None 17. None 18. PQR is an isosceles right triangle, right-angled at Q then the value of2cosecRsecR is: 5 4 1 6 None 19. If x and y are complementary angles, then cos x = cos y sin x = sin y tan x = tan y sec x = cosec y None 20. Assertion: The value of SinA = CosA for all A.Reason: Sin 45º = Cos 45º = 1/√2 Assertion (A) is false but reason (R) is true. Assertion (A) is true but reason (R) is false. Both assertion (A) and reason (R) are true but reason(R) is not the correct explanation of assertion (A). Both assertion (A) and reason (R) are true and reason(R) is the correct explanation of assertion (A). 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