Question

If sin theta is equal to p upon underoot p square+q square ......
Then prove that q sin theta = p cos theta.?

Answer 1

Step-by-step explanation:

Here is your answer. I hope that helps

Answer 2

$pcos\theta=qsin\theta$ proved.

Step-by-step explanation:

Consider the provided information.

$sin\theta=\frac{p}{\sqrt{p^2+q^2} }$

Squaring both sides.

$sin^2\theta=(\frac{p}{\sqrt{p^2+q^2} })^2$

$sin^2\theta=\frac{p^2}{p^2+q^2}$

$1-cos^2\theta=\frac{p^2}{p^2+q^2}$ (∴sin²θ=1-cos²θ)

$cos^2\theta=1-\frac{p^2}{p^2+q^2}$

$cos^2\theta=\frac{p^2+q^2-p^2}{p^2+q^2}$

$cos^2\theta=\frac{q^2}{p^2+q^2}$

$cos\theta=\frac{q}{\sqrt{p^2+q^2}}$

Multiply the above equation with p.

$pcos\theta=\frac{pq}{\sqrt{p^2+q^2}}$......(1)

And multiply the provided equation with q.

$qsin\theta=\frac{pq}{\sqrt{p^2+q^2} }$......(2)

From equation 1 and 2.

$pcos\theta=qsin\theta$

Hence,  proved

#Learn more

Prove the trigonometric identity 1+ cot square A= cosec square A

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