Question

if sin 5 theta is equals to cos 4 theta where 5 theta and 4 theta acute angles find the value of theta

Answer 1

A/c to question,
sin5∅ = cos4∅

we know,
sin∅ = cos( 90- ∅) use , this here,

cos( 90° - 5∅) = cos4∅

we also know ,
if CosA = cosB
then,
A = B use, this

(90 -5∅) = 4∅

90° = 5∅ + 4∅

90° = 9∅

∅ = 90°/9 = 10°

hence, theta = 10°

Answer 2

Hi friend,

sin5θ=cos4θ

But cosθ=sin(90-θ)

So,

sin5θ=sin(90-4θ)

If sinα=sinβ
⇒⇒⇒α=β

5θ=90-4θ
9θ=90
θ=10.

HOPE THIS HELPS....