Question

Question #08ca1

Answer 1

`LHS=(sec x sin x)/(tan x + cot x)`

`=(sec x sin x)/(sinx/cosx + cos x/sinx)`

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

`=secx*sinx*cosx*sinx`

`=sin^2x`

Answer 2

see explanation.

Explanation:

Making use of the following `color(blue)"trigonometric identities"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(tanx=sinx/cosx,cotx=cosx/sinx)color(white)(2/2)|)))`

`"and " color(red)(bar(ul(|color(white)(2/2)color(black)(secx=1/cosx)color(white)(2/2)|)))`

`"left side "=(secx xx sinx)/(tanx+cotx)`

`color(white)(xxxxxx)=(sinx/cosx)/(sinx/cosx+cosx/sinx)`

`color(white)(xxxxxx)=(sinx/cosx)/((sin^2x+cos^2x)/(sinxcosx))`

`color(white)(xxxxxx)=sinx/cancel(cosx) xx(sinxcancel(cosx))/1`

`color(white)(xxxxxx)=sin^2x="right side"rArr" verified"`