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.
APPEARS IN
संबंधित प्रश्न
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
