The value of sin - - cosec-2 - cos - - sec-2 - tan2- - cot2- is

(sin θ + cosecθ)^2 + (cos nbsp;θ + secθ)^2 – (tan^2θ + cot^2θ) =sin^2 θ + cosec^2θ+2 sin nbsp;θ cosecθ + cos^2 θ + sec^2 θ+2 cos nbsp; θ sec nbsp; θ t ...

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Byju's Answer

Standard XII

Physics

Introduction

The value of ...

Question

The value of $(s i n θ + c o s e c θ)^{2} + (c o s θ + s e c θ)^{2} - (t a n^{2} θ + c o t^{2} θ)$ is

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Solution

The correct option is D 7
$(s i n θ + c o s e c θ)^{2} + (c o s θ + s e c θ)^{2} - (t a n^{2} θ + c o t^{2} θ)$

$= s i n^{2} θ + c o s e c^{2} θ + 2 s i n θ c o s e c θ + c o s^{2} θ + s e c^{2} θ + 2 c o s θ s e c θ - t a n^{2} θ - c o t^{2} θ$

= $(s i n^{2} θ + c o s^{2} θ) + (c o s e c^{2} θ - c o t^{2} θ) + (s e c^{2} θ - t a n^{2} θ) + 2 s i n θ \times \frac{1}{s i n θ} + 2 c o s θ \times \frac{1}{c o s θ}$

=1+1+1+2+2

=7

Suggest Corrections

The value of (sinθ+cosecθ)2+(cosθ+secθ)2–(tan2θ+cot2θ) is

The correct option is D 7(sinθ+cosecθ)2+(cosθ+secθ)2–(tan2θ+cot2θ) =sin2θ+cosec2θ+2sinθcosecθ+cos2θ+sec2θ+2cosθsecθ−tan2θ−cot2θ =(sin2θ+cos2θ)+(cosec2θ−cot2θ)+(sec2θ−tan2θ)+2sinθ×1sinθ+2cosθ×1cosθ =1+1+1+2+2 =7

The value of $(s i n θ + c o s e c θ)^{2} + (c o s θ + s e c θ)^{2} - (t a n^{2} θ + c o t^{2} θ)$ is