Question

find the value of cos theta cos 90 minus theta minus sin theta sin 90 minus theta

Answer 1

Cos∅ cos ( 90 - ∅ ) - sin∅ sin ( 90 - ∅ )

=> Sin∅ = cos ( 90 - ∅ )

=> Cos∅ = sin ( 90 - ∅ )


Cos∅ Sin∅ - Sin∅ Cos∅

= 0

Answer 2

Answer:

Value of $cos\theta cos(90-\theta)-sin\theta sin(90-\theta)$ = 0

Explanation:

Method 1 :

We know that,

$\boxed {cosAcosB-sinAsinB\\=cos(A+B)}$

Here,

Given $cos\theta cos(90-\theta)-sin\theta sin(90-\theta)$

=$cos(\theta+90-\theta)$

=$cos90$

= 0 \* cos 90° = 0 *\

Therefore,

Value of $cos\theta cos(90-\theta)-sin\theta sin(90-\theta)$ = 0

Method 2:

i)$cos(90-\theta) = sin\theta$ ---(1)

ii) $sin(90-\theta)=cos\theta$----(2)

Now ,

$cos\theta cos(90-\theta)-sin\theta sin(90-\theta)$

= $cos\theta sin\theta-sin\theta cos\theta$

/* from(1) and (2) */

= $0$

••••

•••