Advertisements
Advertisements
Question
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
Advertisements
Solution
L.H.S. = cos A (1 + cot A) + sin A (1 + tan A)
= `cosA(1 + cosA/sinA) + sinA(1 + sinA/cosA)`
= `(cosA(sinA + cosA))/sinA + (sinA(cosA + sinA))/cosA`
= `(sinA + cosA)[cosA/sinA + sinA/cosA]`
= `(sinA + cosA)[(cos^2A + sin^2A)/(sinAcosA)]`
= `(sinA + cosA) xx 1/(sinAcosA)`
= `(sinA + cosA)/(sinAcosA)` ...[∵ cos2θ + sin2θ = 1]
= `sinA/(sinAcosA) + cosA/(sinAcosA)`
= `1/cosA + 1/sinA`
= sec A + cosec A = R.H.S.
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
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
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
Simplify : 2 sin30 + 3 tan45.
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
