Question

Sec alpha - cosec 9 alpha =0
Find Sin 10 alpha​

Answer 1

Answer:

1

Step-by-step explanation:

$\sec( \alpha ) - \csc( 9 \alpha ) = 0 \\ \sec( \alpha ) = \csc(9 \alpha ) \\ \csc(90 - \alpha ) = \csc(9 \alpha ) \\ (90 - \alpha ) = 9 \alpha \\ 10 \alpha = 90 \\ \alpha = 9 \\ therefore \\ \sin( 10 \alpha ) = \sin(10 \times 9) \\ \sin(90) = 1$

Answer 2

The value of $\sin 10 \alpha$  is equal to 1.

Step-by-step explanation:

We have,

$\sec \alpha-\csc 9\alpha =0$

To find, the value of $\sin 10 \alpha$ = ?

∴ $\sec \alpha-\csc 9\alpha =0$

⇒ $\sec \alpha=\csc 9\alpha$

⇒ $\sec \alpha=\sec (90- 9\alpha)$

Using the trigonometric identity,

$\sec A=\csc (90- A)$

∴ α = 90° - 9α

⇒ α + 9α = 90°

⇒ 10α = 90°

Dividing both sides by 10, we get

⇒ α = 9°

∴ $\sin 10 \alpha$

$=\sin 10 (9)$

$=\sin 90$

= 1

Thus, the value of $\sin 10 \alpha$  is equal to 1.