Evaluate the following :cos54∘sin36∘−cos36∘sin54∘

We have,cos54∘sin36∘−cos36∘sin54∘=cos54∘sin(90∘−54∘)−cos36∘sin(90∘−36∘)=cos54∘cos54∘−cos36∘cos36∘=1−1=0 [∵sin(90∘−θ)=cosθ,cos(90∘−θ)=sinθ]

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Evaluate the following : {sin 36^{}}{cos 54^{}} , - , {sin 54^

Question

Evaluate the following :
$\frac{s in 3 6 ^{\circ}}{cos 5 4 ^{\circ}} - \frac{s in 5 4 ^{\circ}}{cos 3 6 ^{\circ}}$

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Evaluate the following :

\frac{s in 3 6 ^{\circ}}{cos 5 4 ^{\circ}} - \frac{s in 5 4 ^{\circ}}{cos 3 6 ^{\circ}}

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We have,

\frac{s in 3 6 ^{\circ}}{cos 5 4 ^{\circ}} - \frac{s in 5 4 ^{\circ}}{cos 3 6 ^{\circ}} = \frac{s in ( 9 0 ^{\circ} - 5 4 ^{\circ} )}{cos 5 4 ^{\circ}} - \frac{s in ( 9 0 ^{\circ} - 3 6 ^{\circ} )}{cos 3 6 ^{\circ}} = \frac{cos 5 4 ^{\circ}}{cos 5 4 ^{\circ}} - \frac{cos 3 6 ^{\circ}}{cos 3 6 ^{\circ}} = 1 - 1 = 0

[∵ s in (9 0^{\circ} - θ) = cos θ, cos (9 0^{\circ} - θ) = s in θ]

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Question Text	Evaluate the following : $\frac{s in 3 6 ^{\circ}}{cos 5 4 ^{\circ}} - \frac{s in 5 4 ^{\circ}}{cos 3 6 ^{\circ}}$
Answer Type	Text solution:1
Upvotes	150