Question

sin square theta + cos square theta=1​

Answer 1

Answer:

yes, sin ^2theta+cos^2theta=1

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Answer 2

Sin theta = perpendicular/hypotenuse

therefore, sin ^2 theta = perpendicular ^2/ hypotenuse ^2.

similarly,

cos theta = base / hypotenuse

cos ^2 theta = base^2 / hypotenuse ^2

given, sin ^2 theta + cos ^2 theta

= perp.^2/ hypotenuse ^2 + base^2 / hypotenuse ^2

= (perp.^2 + base^2) / hypotenuse ^2 ................... (i)

= now we know that in a right angled triangle, by pythagoras theorem, hypotenuse ^2 = perp.^2 + base^2

so, putting this in (i),

we get , hypotenuse ^2 / hypotenuse ^2

= 1

therefore hence proved

as LHS= RHS.

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