Dear student,sec2θ+cosec2θ=tanθ+cotθLHSsec2θ+cosec2θ=1+tan2θ+1+cot2θ∵1+tan2A=sec2A and 1+cot2A=cosec2A also we know that tanA×cotA=1=1+tan2θ+1+cot2θ=tan2θ+cot2θ+2=tan2θ+cot2θ+2tanθ×cotθ=tanθ+cotθ2=tanθ+cotθ=RHSRegards

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D e a r s t u d e n t, \sqrt{s e c^{2} θ + \cos e c^{2} θ} = \tan θ + co t θ L H S \sqrt{s e c^{2} θ + \cos e c^{2} θ} = \sqrt{1 + \tan^{2} θ + 1 + co t^{2} θ} (∵ 1 + \tan^{2} A = s e c^{2} A a n d 1 + c o t^{2} A = \cos e c^{2} A) a l s o w e k n o w t h a t \tan A \times c o t A = 1 = \sqrt{1 + \tan^{2} θ + 1 + co t^{2} θ} = \sqrt{\tan^{2} θ + co t^{2} θ + 2} = \sqrt{\tan^{2} θ + co t^{2} θ + 2 \tan θ \times c o t θ} = \sqrt{{(\tan θ + co t θ)}^{2}} = \tan θ + co t θ = R H S R e g a r d s

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