Advertisements
Advertisements
Question
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
Advertisements
Solution
`(sinA - cosA)(1 + tanA + cotA)`
= `sinA + (sin^2A)/cosA + cosA - cosA - sinA - (cos^2A)/sinA`
= `(sin^2A)/cosA - (cos^2A)/sinA`
= `secA/(cosec^2A) - (cosecA)/(sec^2A)`
RELATED QUESTIONS
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
