Home
Class 10
MATHS
Prove the following identity, where the...

Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(iv) `(1+secA)/(secA)=(sin^2A)/(1-cosA)`

Text Solution

Verified by Experts

First, find the simplified form of L.H.S
L.H.S. = `(1 + sec A)/sec A`
Since secant function is the inverse function of cos function and it is written as
`= (1 + 1/cos A)/(1/cos A)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove the following identity,where the angles invorved are acute angles for which the expressions are defined.(ii) (cos A)/(1+sin A)+(1+sin A)/(cos A)=2sec A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.( ix) (csc A-sin A)(sec A-cos A)=(1)/(tan A+cot A)[ Hint : Simplify L.HS and RHS separately]

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(viii) (sin A+cos ecA)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(vi) sqrt((1+sin A)/(1-sin A))=sec A+tan A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(i) (csc theta-cot theta)^(2)=(1-cos theta)/(1+cos theta)

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(cos A-sin A+1)/(cos A+sin A-1)=cos ecA+cot A

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(x) ((1+tan^(2)A)/(1+cot^(2)A))=((1-tan A)/(1-cot A))^(2)=tan^(2)A

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (vii) (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta

Prove the following identity,where the angles involved are acute angles for which the expressions are defined.(iii) (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta cos ec theta

Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (sin theta - 2 sin^3 theta)/(2 cos^3 theta - cos theta)= tan theta