Question

if sin theta + cos theta equal to P and sin theta minus cos theta equal to Q then​

Answer 1

Step-by-step explanation:

Sin A + Cos A = P

Sin A - Cos A = Q

2SinA = P+Q

SinA = (P+Q)/2

2Cos A = P-Q

Cos A = (P-Q)/2

Answer 2

The relation between P and Q is $P^2+Q^2=2$.

Step-by-step explanation:

We have,

$\sin \theta +\cos \theta =P$                              .......(1)

Also, $\sin \theta -\cos \theta =Q$                     .......(2)

To find, the relation between P and Q.

Squaring and adding equations (1) and (2), we get

$(\sin \theta +\cos \theta)^2+(\sin \theta -\cos \theta)^2=P^2+Q^2$

⇒ $\sin^2 \theta +\cos^2 \theta+2\sin \theta\cos \theta+\sin^2 \theta +\cos^2 \theta-2\sin \theta\cos \theta=P^2+Q^2$

⇒ $\sin^2 \theta +\cos^2 \theta+\sin^2 \theta +\cos^2 \theta=P^2+Q^2$

⇒ $(\sin^2 \theta +\cos^2 \theta)+(\sin^2 \theta +\cos^2 \theta)=P^2+Q^2$

Using the trigonometric identity,

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

$1+1=P^2+Q^2$

⇒ $P^2+Q^2=2$

Thus, the relation between P and Q is $P^2+Q^2=2$.