Advertisements
Advertisements
प्रश्न
If A and B are complementary angles, prove that:
`(sinA + sinB)/(sinA - sinB) + (cosB - cosA)/(cosB + cosA) = 2/(2sin^2A - 1)`
Advertisements
उत्तर
Since, A and B are complementary angles, A + B = 90°
`(sinA + sinB)/(sinA - sinB) + (cosB - cosA)/(cosB + cosA)`
= `(sinA + sinB)/(sinA - sinB) + (cos(90^@ - A) - cos(90^@ - B))/(cos(90^@ - A) + cos(90^@ - B))`
= `(sinA + sinB)/(sinA - sinB) + (sinA - sinB)/(sinA + sinB)`
= `((sinA + sinB)^2 + (sinA - sinB)^2)/((sinA - sinB)(sinA + sinB)`
= `(sin^2A + sin^2B + 2sinAsinB + sin^2A + sin^2B - 2sinA)/(sin^2A - sin^2B`
= `2(sin^2A + sin^2B)/(sin^2A - sin^2B)`
= `2(sin^2A + sin^2(90^@ - A))/(sin^2A - sin^2(90^@ - A))`
= `2(sin^2A + cos^2B)/(sin^2A - cos^2B)`
= `2/(sin^2A - (1 - sin^2A))`
= `2/(2sin^2A - 1)`
संबंधित प्रश्न
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Prove the following trigonometric identities.
(secθ + cosθ) (secθ − cosθ) = tan2θ + sin2θ
if `cos theta = 4/5` find all other trigonometric ratios of angles θ
if `cot theta = sqrt3` find the value of `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`
Evaluate:
tan(55° - A) - cot(35° + A)
Find the value of x, if sin x = sin 60° cos 30° + cos 60° sin 30°
Evaluate:
`(5sin66^@)/(cos24^@) - (2cot85^@)/(tan5^@)`
If 4 cos2 A – 3 = 0 and 0° ≤ A ≤ 90°, then prove that cos 3 A = 4 cos3 A – 3 cos A
If \[\cos \theta = \frac{2}{3}\] find the value of \[\frac{\sec \theta - 1}{\sec \theta + 1}\]
In ∆ABC, `sqrt(2)` AC = BC, sin A = 1, sin2A + sin2B + sin2C = 2, then ∠A = ? , ∠B = ?, ∠C = ?
