Question 11

If sec θ – sec² θ = 1, then what is the value of tan² θ – tan⁴θ ?

Solution

sec θ – sec² θ = -1

Question 12

If sin θ – cos θ = 0, then what is the value of sin⁴ θ + cos⁴θ ?

Solution

sin⁴ θ + cos⁴θ = 1/2

Question 13

If k + 1 = sec² θ(1 + sin θ )(1- sin θ ), find the value of k

Solution

0(zero)

Question 14

If sin 3θ = cos (θ – 6°), where 3θ and (θ- 6) ° are both acute angles, find the value of θ

Solution

24°

Question 15

If cos² 𝜃 – sin² 𝜃 = tan² 𝜃, prove that 𝑐𝑜𝑠 𝜙 = 1/√2 cosθ

Solution

√2 cosθ = sec𝜃
√2 cosθ = 1/ cos𝜃
cos𝜃 = 1/√2 cosθ

SELF ASSESSMENT

Q1. Consider a right triangle with one angle measuring 45 degrees. The hypotenuse
is 10 units long. Calculate the lengths of the other two sides using trigonometric
ratios.
Q2. The ratio of the sine of an angle to its cosine is 8:15. Find their actual value.

Q3. Mohan finds a trigonometric equation in which the value of the unknown variable K was not given. If k + 1 = Sec ² 𝜃 (1 + sin 𝜃) (1- sin 𝜃) was the equation then find the value of k with the help of the trigonometric identities

Q4. Consider a right triangle with one angle measuring 45 degrees. The hypotenuse is 10 units long. Calculate the lengths of the other two sides using trigonometric ratios

Q5. The ratio of the sine of an angle to its cosine is 8:15. Find their actual value