Question

prove : cot2 @ - tan2 @ =cosec2 @ - sec2@ by the following given steps
(a) consider LHS and write the square raletion of cot2 @ and tan2 @
(b) simplify and prove it equal to RHS​

Answer 1

Answer:

Cot^2 @ - Tan^2 @ = Cosec ^2 @ - Sec^2 @

Step-by-step explanation:

Cot^2 @ - Tan^2 @ = Cosec ^2 @ - Sec^2 @

LHS:-

cos^2 @ - sin^2 @

sin @^2 cos^2 @

cos^4 @ - sin^4 @

sin^2 @ cos^2 @

(cos^2 @ + sin^2 @)(cos^2 @ - sin^2 @)

sin^2 @ cos^2 @

1 (cos^2 @ - sin^2 @)

sin^2@ cos^2 @

cos^2 - sin^2 @

sin^2@ cos^2 @ sin^2@ cos^2 @

1 - 1

sin^2@ cos^2 @

Cosec ^2 @ - Sec^2 @

LHS = RHS

Hence proved.

Hope it helps you....

Answer 2

Cot^2 @ Tan^2 @ = Cosec ^2 @ - Sec^2 @

Step-by-step explanation:

Cot^2 @ Tan^2 @ = Cosec ^2 @ - Sec^2 @

LHS:

cos^2 @sin^2 @

sin @^2 cos^2 @

cos^4 @- sin^4 @

sin^2 @ cos^2 @ (cos^2 @ + sin^2 @)(cos^2 @ - sin^2 @)

1 (cos^2 @- sin^2 @)

sin^2 @ cos^2 @ sin^2@ cos^2 @ - sin^2 @ 1 1 cos^2 @

cos^2

sin^2@ cos^2 @ sin^2@ cos^2 @

sin^2@

Cosec ^2 @ - Sec^2 @

LHS = RHS