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If 5θ and4θ are acute angles satisfying sin 5θ=cos 4θ then,the value of 2 sinθ- √3 tan3θ is​

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Question:-

If 5θ and4θ are ACUTE angles satisfying sin 5θ=cos 4θ then,the VALUE of 2 sinθ- √3 tan3θ is

{\pink{\underline{\underline{\bold{Answer:-}}}}}

Given : sin 5θ = cos 4θ  and  5θ and 4θ  are acute angles.

sin 5θ = cos 4θ

cos (90° - 5θ) = cos 4θ  

[cos (90° - θ) = sin θ]

On equating both sides,

(90° - 5θ) =  4θ  

90°  =  5θ +  4θ  

90° = 9θ

θ = 90°/9

θ = 10°  

The value of 2 sin 3θ  - √3 tan 3θ :  

= 2 sin 3 (10°) - √3 tan 3(10°)

= 2 sin 30° - √3 tan 30°

= 2 (½) - √3 (1/√3)

[sin 30° = ½ , tan 30° = 1/√3]

= 1 - 1

= 0  

2 sin 3θ - √3 tan 3θ = 0

Hence, the value of 2 sin 3θ - √3 tan 3θ is 0 .

hope it HELPS you..


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