Question

Prove that Sin 5-cos 25=cos 35

Answer 1

$\underline{\textsf{To prove:}}$

$\mathsf{sin\,5-cos\,25=-cos\,35}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{sin\,5-cos\,25}$

$\textsf{using}$

$\boxed{\mathsf{cos\,\theta=sin(90-\theta)}}$

$\mathsf{=sin\,5-sin(90-25)}$

$\mathsf{=sin\,5-sin\,65}$

$\textsf{Using}$

$\boxed{\mathsf{sinC-sinD=2\,cos(\frac{C+D}{2})\,sin(\frac{C-D}{2})}}$

$\mathsf{=2\,cos(\frac{5+65}{2})\,sin(\frac{5-65}{2})}$

$\mathsf{=2\,cos(\frac{70}{2})\,sin(\frac{-60}{2})}$

$\mathsf{=2\,cos\,35\,sin(-30)}$

$\mathsf{=-2\,cos\,35\,sin\,30}$

$\mathsf{=-2\,cos\,35(\frac{1}{2})}$

$\mathsf{=-cos\,35}$

$\implies\boxed{\mathsf{sin\,5-cos\,25=-cos\,35}}$

Find more:

PROVE THAT:

cos 12 cos 24 cos 36 cos 48 Cos 60 cos 72 cos 84 equal = 1 / 128​

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