Question

if tanø=1/√3,find 7 sin²ø+3cos²ø​

Answer 1

Answer is 4. Refer to the solution given

Answer 2

Given :

tanθ=1/√3

To find :

The value of 7sin ²θ+3cos²θ

Solution :

We have,$\sf\tan\theta=\dfrac{1}{\sqrt{3}}$

$\implies\theta=30\degree$

Let's look at some values

$\begin{array}{| c | c | c | c | c | c |}\cline{1-6} \bf Angles & \bf 0^{o} & \bf 30^{o} & \bf 45^{o} & \bf 60^{o} & \bf 90^{o} \\\cline{1-6} \tt Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}}& \dfrac{\sqrt{3}}{2}& 1\\\cline{1-6} \tt cos \theta & 1 & \dfrac{\sqrt{3}}{2} &\dfrac{1}{\sqrt{2}}&\dfrac{1}{2}&0\\\cline{1-6} \tt tan \theta & 0 & \dfrac{1}{\sqrt{3}} & 1& \sqrt{3} & \infty \\\cline{1-6} \tt cosec \theta & \infty & 2 & \sqrt{2} & \dfrac{2}{\sqrt{3}} &1\\\cline{1-6} \tt sec \theta & 1 & \dfrac{2}{\sqrt{3}} & \sqrt{2} & 2 & \infty \\\cline{1-6} \tt cot \theta & \infty & \sqrt{3} &1& \dfrac{1}{\sqrt{3}} &0\\\cline{1-6}\end{array}$

Here, '$\red{\infty}$' stands for

undefined(not defined) values.

$\rule{200}2$

$\sf7\sin\theta+3\cos^230\theta$

$\sf=7\sin^230\degree+3\cos^230\degree$

$\sf=7\times[\dfrac{1}{2}]^2+3[\dfrac{\sqrt{3}}{2}]^2$

$\sf=7\times\dfrac{1}{4}+3\times\dfrac{3}{4}$

$\sf=\dfrac{16}{4}=4$