Question

if cos 8 theta = sin theta and 8 theta Is greater than 90 then sec6 theta=
​

Answer 1

SOLUTION

GIVEN

cos 8θ = sin θ and 8θ < 90°

TO DETERMINE

The value of sec 6θ

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

cos (90° - θ) = sin θ

EVALUATION

Here it is given that

cos 8θ = sin θ

⇒ cos 8θ = cos (90° - θ)

⇒ 8θ = 90° - θ

⇒ 8θ + θ = 90°

⇒ 9θ = 90°

⇒ θ = 10°

Now

sec 6θ

= sec ( 6 × 10°)

= sec 60°

= 2

FINAL ANSWER

Hence the required value sec 6θ = 2

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