Question

इज इक्वल टू 1 प्लस साइन एक्स वाई वन माइनस कॉस एक्स प्लस साइन एक्स ​वेयर इज इक्वल

Answer 1

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

To prove : sin²θ + cos²θ = 1

Proof :

In a triangle using sine rule we know that :

\sin\theta=\frac{Perpendicular}{Hypotenuse}\\\\\implies \sin^2\theta= \frac{Perpendicular^2}{Hypotenuse^2}........(1)\\\\\cos\theta=\frac{Base}{Hypotenuse}\\\\\implies \cos^2\theta= \frac{Base^2}{Hypotenuse^2}......(2)\\\\\text{Now, adding (1) and (2)}\\\\\implies \sin^2\theta+\cos^2 \theta =\frac{Perpendicular^2}{Hypotenuse^2} + \frac{Base^2}{Hypotenuse^2} \\\\\implies \sin^2\theta+\cos^2 \theta =\frac{Perpendicular^2+Base^2}{Hypotenuse^2}\\\\\implies \sin^2\theta+\cos^2 \theta =\frac {Hypotenuse^2}{Hypotenuse^2}\\\\\implies \sin^2\theta+\cos^2 \theta =1

Explanation:

Theta is written as A

To prove : sin^2A + cos^2A

===================

Proof :

We know, sin^2 A = \frac{height^2}{hyotenuse^2} \\ \\cos^2 A = \frac{base^2}{hypotenuse^2}

Then,

sin^2 A + cos^2 A

\frac{height^2}{hypotenuse^2} + \frac{base^2}{hypotenuse^2} \\ \\ \frac{height^2 + base^2}{hypotenuse^2} \\ \\ \frac{hypotenuse^2}{hypotenuse^2} \\ \\ 1

Hence, Proved.

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