Question

If sintheta+costheta=p then show that Psquare-1/p=sintheta

Answer 1

Answer:

Step-by-step explanation:

Since we know that p = sin Q + cos Q we want to prove that p square -1/2 = sinQ x cosQ.

Then lets star by considering what is given.

p = sin Q + cos Q

Thus:

$p^{2}$ = $sin^{2}Q$ + $cos^{2}Q$ + 2sinQ x cosQ

This is the same as saying that p square is equal to one plus two times sinus of Q times cosines of Q.

$p^{2}$ = 1 + 2sinQ x cosQ

$p^{2}$ - 1 = 2sinQ x cosQ

$p^{2}$ -1/2 = sinQ x cosQ

What we have to take in consideration and it will be really useful here is the fundamental theorem of trigonometry, which says the following:

$sin^{2}Q + cos^{2}Q = 1$

Hence proved.