Question

If $tan\theta =4/3$, show that $(sin\theta +cos\theta )=7/5$

Answer 1

Given,

$tan\theta =4/3.$

$cot\theta =1/\left(4/3\right)=3/4$

[ Since, $1/tan\theta =cot\theta$ ]

We know that,

$tan\theta =$ opposite side to theta / adjacent side to theta.

So, opposite side $=4$ , Adjacent side $=3$

Hypotenuse = $\sqrt{(4²+3²)}=5$

Now,

$sin\theta =$ Opposite side to theta / Hypotenuse $=4/5$

$cos\theta =$ Adjacent side to theta / Hypotenuse $=3/5$

To prove : $sin\theta +cos\theta =7/5.$

L. H.S

$=sin\theta +cos\theta$

$=4/5+3/5$

$=7/5$

= R. H. S

Hence proved!