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.
(i) `(cosectheta-cottheta)^2=(1-costheta)/(1+costheta)`

Text Solution

Verified by Experts

`(cosecθ - cotθ)² = (1 - cosθ) / (1 + cosθ)`
L.H.S =` (cosecθ - cotθ)^2` .....(1)
We know that the trigonometric functions,
`cot (x) = cos (x)/sin (x) = 1/tan (x)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (iii) (tantheta)/(1-cottheta)+(cottheta)/(1-tantheta)=1+sectheta cosectheta

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. (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. (iv) (1+secA)/(secA)=(sin^2A)/(1-cosA)

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. sqrt((1+sinA)/(1-sinA))=secA+tanA

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (v) (cosA-sinA+1)/(cosA+sinA-1)=cosec A+cotA

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (cosA)/(1+sinA)+(1+sinA)/(cosA)=2secA

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

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (viii) (sinA+cose c A)^2+(cosA+secA)^2=7+tan^2A+cot^2A

Prove the following identity, where the angles involved are acute angles for which the expressions are defined. (ix) (c o s e c\ A\ \ sin\ A)(secA-cosA)=1/(tanA+cotA) [Hint : Simplify LHS and RHS separately]