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प्रश्न
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
उत्तर
L.H.S. = x2 + y2 + z2
= (r sin A cos B)2 + (r sin A sin B)2 + (r cos A)2
= r2 sin2 A cos2 B + r2 sin2 A sin2 B + r2 cos2 A
= r2 sin2 A (cos2 B + sin2 B) + r2 cos2 A
= r2 (sin2 A + cos2 A)
= r2 = R.H.S.
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Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
