Advertisements
Advertisements
प्रश्न
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Advertisements
उत्तर
L.H.S. = `(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB)`
= `((sinA - sinB)(sinA + sinB) + (cosA - cosB)(cosA + cosB))/((cosA + cosB)(sinA + sinB)`
= `(sin^2A - sin^2B + cos^2A - cos^2B)/((cosA + cosB)(sinA + sinB))`
= `((sin^2A + cos^2A) - (sin^2B + cos^2B))/((cosA + cosB)(sinA + sinB))` ...[∵ cos2 A + sin2 A = 1]
= `(1 - 1)/((cosA + cosB)(sinA + sinB))`
= 0 = R.H.S.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
If tan θ × A = sin θ, then A = ?
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3
