Question

if √3 tan= 1 then find and write complementary angle of it.​

Answer 1

tan@=tan30
@=30

Then complement angle of 30

Answer 2

Solution:-

$: \implies \: \: \rm \: if \: \sqrt{3} \tan \theta = 1$

$: \implies \rm \tan\theta = \dfrac{1}{ \sqrt{3} } = \dfrac{p}{b}=30⁰$

 

Using phythogoeros theorem

$: \implies \rm \: p = 1 \: \: b = \sqrt{3} \: \: and \: \: h = x$

$: \implies \rm \: {h}^{2} = {p}^{2} + {b}^{2}$

$: \implies \rm {x}^{2} = {1}^{2} + (\sqrt{3} ) {}^{2}$

$: \implies \: \rm {x}^{2} = 1 + 3$

$: \implies \: \rm {x}^{2} = 4$

$: \implies \: \rm \: x = 2 = h$

$: \implies \rm \: p = 1 \: \: b = \sqrt{3} \: \: and \: \: h = 2$

All  complementary angle  are

$: \implies \rm \sin\theta = \dfrac{p}{h}  = \dfrac{1}{2}$

$: \implies \rm \cos \theta = \dfrac{b}{h} = \dfrac{ \sqrt{3} }{2}$

$: \implies \rm \tan\theta = \dfrac{p}{b} = \dfrac{1}{ \sqrt{3} }$

$: \implies \rm \csc \theta = \dfrac{h}{p} = \dfrac{2}{1}$

$: \implies \rm \sec\theta = \dfrac{h}{b} = \dfrac{2}{ \sqrt{3} }$

$: \implies \rm \: \cot \theta = \dfrac{b}{p} = \dfrac{ \sqrt{3} }{1}$