Question

(iv) Vsec? 0 + cosec?0 = tan 0 + cot0​

Answer 1

Correct Question :-

• $\sf{sec \: \theta + cosec \: \theta = tan \: \theta \cdot cot \: \theta}$

Answer :-

We have,

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀• L.H.S = sec θ + cosec θ

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀• R.H.S = tan θ · cot θ

⠀⠀⠀⠀⠀ ⠀⠀⠀__________________

$\\ \sf{\longrightarrow \: sec \: \theta \cdot cosec \: \theta}$

By putting the identity [secθ = 1/cosθ] and [cosescθ = 1/sinθ], We get,

$\\ \sf{\longrightarrow \: \dfrac{1}{cos \: \theta \: \cdot \: sin \: \theta}}$

By putting the identity [sin²θ + cos²θ = 1], We got,

$\\ \sf{\longrightarrow \: \dfrac{{sin}^{2} \: \theta + {cos}^{2} \: \theta}{cos \: \theta \: \cdot \: sin \: \theta}}$

By evaluating,

$\\ \sf{\longrightarrow \: \dfrac{sin \: \theta}{cos \: \theta} + \dfrac{cos \: \theta}{sin \: \theta}}$

By putting the identity [sinθ/cosθ = tanθ] and [cosθ/sinθ = cotθ], We got,

$\\ \sf{\longrightarrow \: tan \: \theta + cot \: \theta = R.H.S}$

Hence, Proved!