Question

Evaluate: sin theta . Sec( 90 degree- theta) SHARE

Answer 1

SinΦ.sec(90-Φ)

We know that,

Sec(90-Φ)=cosecΦ

So,

SinΦ.cosecΦ

And we also know that,

CosecΦ= 1/sinΦ

Since,

SinΦ.1/sinΦ

=1

Answer 2

Answer:

$\sin\theta\cdot \sec(90-\theta)=1$

Step-by-step explanation:

Given : Expression $\sin\theta\cdot \sec(90-\theta)$

To find : Evaluate the expression ?

Solution :

Expression $\sin\theta\cdot \sec(90-\theta)$

Substitute,  $\sec(90-\theta)=\csc\theta$

$\sin\theta\cdot \sec(90-\theta)=\sin\theta\cdot \csc\theta$

$\sin\theta\cdot \sec(90-\theta)=\sin\theta\cdot \frac{1}{\sin\theta}$

$\sin\theta\cdot \sec(90-\theta)=1$

Therefore, The value is  $\sin\theta\cdot \sec(90-\theta)=1$