Convert LHS into sine, cosine ⇒ #160; sinθcosθ +cosθsinθ ⇒ #160; sin^2θ + cos^2 θsinθ cosθ ⇒ #160; 2×12sinθ cosθ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Trigonometric Ratios of Common Angles

tanθ +θ = 2 2...

Question

$tan θ + cot θ = 2 csc 2 θ$

Open in App

Solution

Convert LHS into $s i n e, c o s i n e$

$\Rightarrow$ $\frac{s i n θ}{c o s θ} + \frac{c o s θ}{s i n θ}$

$\Rightarrow$ $\frac{s i n^{2} θ + c o s^{2} θ}{s i n θ c o s θ}$

$\Rightarrow$ $\frac{2 \times 1}{2 s i n θ c o s θ}$

$\Rightarrow$ $\frac{2}{s i n 2 θ}$

$\Rightarrow$ $2 c o s e c 2 θ$ = RHS

Hence proved

Suggest Corrections

Similar questions

cot θ - tan θ = 2 cot 2 θ

tan θ - cot θ = 2 cot 2 θ

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

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

L i m n \to \infty [t a n θ + \frac{1}{2} t a n \frac{θ}{2} + \dots \dots \dots + \frac{1}{2^{n}} t a n \frac{θ}{2^{n}}] =

\tan (\frac{π}{4} + θ) + \tan (\frac{π}{4} - θ) = 2 \sec 2 θ

Join BYJU'S Learning Program