Question

Find the value of sin24^;cos66^+sin66^;cos24^.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of $\sin24.\cos66+\sin66\cos24$ = 1

Step-by-step explanation:

We have,

$\sin24.\cos66+\sin66\cos24$

To find, the value of $\sin24.\cos66+\sin66\cos24$ = ?

∴ $\sin24.\cos66+\sin66\cos24$

= $\sin24.\cos(90-24)+\sin(90-24)\cos24$

Using the trigonometric identity,

$\sin A=\cos (90-A)$ and

$\cos A=\sin (90-A)$

= $\sin24.\sin24+\cos24.\cos24$

=  $\sin^224+\cos^224$

Using the trigonometric identity,

$\sin^2A+\cos^2A$ = 1

= 1

∴ The value of $\sin24.\cos66+\sin66\cos24$ = 1

Thus, the value of $\sin24.\cos66+\sin66\cos24$ = 1

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