Question

Prove :sin²θ + cos²θ = 1thankyou ~​

Answer 1

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

$\sf\longrightarrow sin^2\theta + cos^2\theta = 1$

Imagine a right angled triangle with one of its acute angle as $\theta$ .

• The side opposite to this angle will be perpendicular .
• Also we know that ,

$\sf\longrightarrow sin\theta =\dfrac{p}{h}$

$\sf\longrightarrow cos\theta =\dfrac{b}{h}$

And by Pythagoras theorem ,

$\sf\longrightarrow h^2 = p^2+b^2 \dots (i)$

Where the symbols have their usual meaning.

Now , taking LHS ,

$\sf\longrightarrow sin^2\theta +cos^2\theta$

• Substituting the respective values,

$\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2$

$\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}$

$\sf\longrightarrow \dfrac{p^2+b^2}{h^2}$

• From equation (i) ,

$\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}$

$\sf\longrightarrow \bf 1 = RHS$

Since LHS = RHS ,

Hence Proved !

I hope this helps.