-i- sin2 -952-11-tan2 -952-1-ii- 11-tan2 -952-11-cot2 -952-1

(i) #160;LHS=sin2 #952;+1(1+tan2 #952;) #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160;=si ...

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Range of Trigonometric Ratios from 0 to 90 Degrees

(i) sin2 #9...

Question

(i) $\sin^{2} θ + \frac{1}{(1 + \tan^{2} θ)} = 1$
(ii) $\frac{1}{(1 + \tan^{2} θ)} + \frac{1}{(1 + \cot^{2} θ)} = 1$

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Solution

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(\sin^{2} θ + \frac{1}{1 + \tan^{2} θ})

\sin^{2} θ + \frac{1}{1 + \tan^{2} θ}

\sqrt{1 + t a n^{2} θ} \sqrt{1 + c o t^{2} θ} \sqrt{1 - c o s^{2} θ} \sqrt{1 - s i n^{2} θ} =

$\frac{1}{1 + t a n^{2} θ} + \frac{1}{1 + c o t^{2} θ} =$

Show that none of the following is an identity :

(i) $c o s^{2} θ + c o s θ = 1$ (ii) $s i n^{2} θ + s i n θ = 2$ (iii) $t a n^{2} θ + s i n θ = c o s^{2} θ$

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