Question

If sin 2 theta=cos 3 theta,then cot 5 theta=_________

Answer 1

Important equations....

#) sinθ=cos(90-θ)

According to the problem.....

Sin2θ=cos3θ

sin2θ=sin(90-3θ)

2θ=90-3θ

5θ=90....

WE WANT cot5θ.....

cot5θ=cot90°=0

Answer 2

If sin 2θ = cos 3θ then cot 5θ = 0

Given :

sin 2θ = cos 3θ

To find :

The value of cot 5θ

Formula :

cos θ = sin ( 90° - θ )

Solution :

Step 1 of 2 :

Find the value of θ

sin 2θ = cos 3θ

⇒ sin 2θ = sin ( 90° - 3θ )

⇒ 2θ = 90° - 3θ

⇒ 2θ + 3θ = 90°

⇒ 5θ = 90°

⇒ θ = 18°

Step 2 of 2 :

Find the value of cot 5θ

cot 5θ

= cot ( 5 × 18° )

= cot 90°

= 0

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