Question

${ \cos }^{2} \alpha + { \sin}^{2} \alpha =$
answer
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Answer 1

◇ QUESTION ◇ :-

$sin {}^{2} \alpha + cos { \alpha }^{2} =$

◇ ANSWER◇

Let a, b, c be lengths of a right angled triangle.

By definition,

》sinθ=b/c (hypotenuse/opposite side)

》cosθ=a/c (hypotenuse/adjacent side)

=>sin2θ+cos2θ=c2b2+c2a2=c2a2+b2

● From Pythagoras theorem

》 c2=a2+b2

》 ∴c2a2+b2=1

Hence,

$\sin( {}^{2} \alpha ) + \cos( { }^{2} \alpha ) = 1$

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