Advertisements
Advertisements
प्रश्न
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
उत्तर
m2 + n2
= (x cos A + y sin A)2 + (x sin A – y cos A)2
= x2 cos2 A + y2 sin2 A + 2xy sin A cos A + x2 sin2 A + y2 cos2 A – 2xy sin A cos A
= x2 (cos2 A + sin2 A) + y2 (cos2 A + sin2 A)
= x2 + y2
Hence, x2 + y2 = m2 + n2
APPEARS IN
संबंधित प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If cos (\[\alpha + \beta\]= 0 , then sin \[\left( \alpha - \beta \right)\] can be reduced to
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Choose the correct alternative:
1 + cot2θ = ?
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
