Question

If 7 sin²θ+ cos²θ=44, show that tan=1/√3

Answer 1

Step-by-step explanation:

Dividing both side by cos²θ we get

7tan²θ+1=44sec²θ

since sec²θ=1+tan²θ

putting in eqn 1 we get

7tan²θ+1=44(1+tan²θ)

or,

37tan²θ+43=0

tan²θ=-43/37

the value of tan²θ should be positive,there is something wrong with the question.

Answer 2

Correct question:

If 7 sin²θ+ cos²θ=4, show that tan=1/√3

AnswEr:

$\tt7 sin²θ+ cos²θ=4$

$\tt \implies4sin²θ+3sin²θ+3cos²θ=4$

$\tt \implies4sin²θ+3(sin²θ+cos²θ)=4$

$\tt \implies \: 4sin²θ+3×1=4$

$\tt \implies \: 4sin²θ=4-3$

$\tt \implies4sin²θ=1$

$\tt \implies \: sin²θ= \frac{1}{4}$

$\therefore \tt \: cos²θ=(1-sin²θ) =(1- \frac{1}{4})= \frac{3}{4}$

$\therefore \tt \: tan²θ= \frac{sin²θ}{cos²θ} = \frac{1}{4} \times \frac{4}{1} = \frac{1}{3}$

$\bf \: Hence,tan θ= \frac{1}{ \sqrt{3} }$