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) = a^{2} – b^{2}]

=

[∵ (a + b)^{2}= a^{2} + b^{2} + 2ab]

=

=

[∵ (1 – sin^{2} θ) = cos^{2} θ & (cos^{2} θ + sin^{2} θ) = 1]

=

=

=

= …(ii)

By equations (i) & (ii),

LHS = RHS

Hence, proved.

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