If cos(2 θ + 54º) = sin θ , 0º θ +54º) 1/(cot5θ + sec (5 θ)/2) ?

If cos(2 θ + 54º) = sin θ , 0º θ +54º)…

If cos(2 $\theta$ + 54º) = sin $\theta$ , 0º<(2 $\theta$ +54º)<90º, then what is the value of $\frac{1}{cot5\theta + sec \frac{5 \theta}{2}}$ ?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. $\frac{\sqrt{3}}{3}$

cos(2 $\theta$ + 54º) = sin $\theta$

sin(90 - 2 $\theta$ - 54) = sin $\theta$

36 - 2 $\theta$ = $\theta$

$\theta$ = 12°

= $\frac{1}{cot5\theta + sec \frac{5 \theta}{2}}$ = 1/(cot60 + sec30) = 1/(1/ $\sqrt3$ + 2/ $\sqrt3$ )

= $\sqrt3$ /3.