Q. 274.4( 17 Votes )

Prove that <span

Answer :

To prove:

Taking RHS:


RHS = cosec θ + cot θ


= [ and are the trigonometric properties]


= …(i)


Now solving LHS:


LHS =


=


=


[Rationalizing it by (cos θ + sin θ ) + 1]


=


=


[ (a + b)(a – b) = a2 – b2]


=


[ (a + b)2= a2 + b2 + 2ab]


=


=


[ (1 – sin2 θ) = cos2 θ & (cos2 θ + sin2 θ) = 1]


=


=


=


= …(ii)


By equations (i) & (ii),


LHS = RHS


Hence, proved.


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