Question

Verify the identity.? 1 + sec^2xsin^2x = sec^2x

Show your work.

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)secx=1/cosx" and "sin^2x+cos^2x=1`

`"consider the left side"`

`rArr1+1/cos^2x xxsin^2x`

`=cos^2x/cos^2x+sin^2x/cos^2x`

`=(cos^2x+sin^2x)/cos^2x`

`=1/cos^2x=sec^2x=" right side"rArr" verified"`

Answer 2

We know that,

`(1) tantheta=sintheta/costheta`

`(2)1+Tan^2theta=sec^2theta`

We have,

`1 + sec^2xsin^2x = sec^2x`

`LHS=1 + sec^2xsin^2x ...to` take , `sec^2x=1/cos^2x`

`=1+sin^2x/cos^2x......toApply (1)`

`=1+tan^2x......toApply(2)`

`=sec^2x`

`=RHS`