Question

Prove this question !!!



CLASS 10TH

CHAPTER TRIGONOMETRY !!!

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Answer 1

So it's proved.
Hope it helps you.

Answer 2

Answer:

Step-by-step explanation:

L. H. S=cosA-sinA+1/cosA+sinA-1

Divide the equation with sinA

It will become like this

cosA/sinA-sinA/sin+1/sinA over cosA/sinA+sinA/sinA+1/sinA

Now use identities, cosA/sinA=cotA

1/sinA=cosecA

sinA/sinA=1

=CotA-1+cosecA/cotA+1-cosecA

={CotA-(1-cosecA) }{cotA-(1-cosecA) }/{cotA+(1-cosecA) }{cot A-(1-cosecA) }

=(cotA-1+cosecA) ^2/(cotA) ^2-(1-cosecA) ^2

Use identity a^2+b^2+c^2-2ab-2bc-2ac

=cot^2A+1+cosec^2A-2cotA-2cosecA+2cotAcosecA/cot^2A-(1+cosec^2A-2cosecA)

=2cosec^2A+2cotAcosecA-2cotA-2cosecA/cot^2A-1-cosec^2A+2cosecA

=2cosecA(cosecA+cotA) -2(cotA+cosecA) /cot^2A-cosec^2A-1+2cosecA

=(cosecA+cotA) (2cosecA-2) /-1-1+2cosecA

=(cosecA+cotA) (2cosecA-2) /(2cosecA-2)

Here we cancelled (2cosecA-2) with (2cosecA-2)

=cosecA+cotA

=R.H.S