Question

Hey guys!!
Here is the question!!!​

Answer 1

HEY ❤️

Your answer is in the given attachment.

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Answer 2

Using x instead of theta.

To Prove :- sinx-cosx+1/sinx+cosx-1= 1/secx-tanx

However, We can Prove this by taking L.H.S as well as R.H.S,

Taking, L.H.S,

= sinx-cosx+1/sinx+cosx-1

Dividing the numerator and denominator by cosx.

= (sinx/cosx-cosx/cosx+1/cosx)/(sinx/cosx+cosx/cosx-1/cosx)

= tanx-1+secx/tanx+1-secx

Multiplying both numerator and denominator by (tanx-secx)

=(tanx+secx-1)(tanx-secx)/(tanx-secx+1)(tanx-secx)

= (tan²x-sec²x)-(tanx-secx)/(tanx-secx+1)(tanx-secx)

= (-1)-(tanx-secx)/(tanx-secx+1)(tanx-secx)

= -1-tanx+secx/(tanx-secx+1)(tanx-secx)

= -(1+tanx-secx)/(tanx-secx+1)(tanx-secx)

= -1/tanx-secx

= -1/tanx-secx × -1/-1

= 1/secx-tanx

Hence, R.H.S, Proved.......❤