Q. 47 B4.1( 47 Votes )

Prove the followi

Answer :

To Prove: sintegrate heta -costheta +1/sintegrate heta +costheta -1 = 1/sectheta -tantheta

Dividing the numerator and denominator by cosθ, we get,

Now, we know that,
sec2θ - tan2θ = 1
Therefore, replacing 1 by sec2θ - tan2θ in the numerator only, we get,

As we know,
a2 - b2 = (a-b)(a+b)

= secθ + tanθ
Now, multiplying and dividing by secθ - tanθ, we get,

As we know,
sec2θ - tan2θ = 1

= R.H.S
Hence, proved.

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