Question

if sinA = 3/5 , prove that tanA + 1/cosA = 2 or -2 ? ​

Answer 1

Explanation:-

$\rm \: \sin( A) = \frac{3}{5}$

We have to prove

$\rm \: \tan(A) + \frac{1}{ \cos(A) } = 2 \: \: or \: \: - 2$

$\rm \: \sin( A) = \frac{3}{5} = \frac{p}{h}$

$\rm \: p = 3 \: \: \: \: h = 5 \: \: and \: \: b = x$

Using Pythagoras theorem

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

$\rm \: (5) {}^{2} = (3) {}^{2} + {x}^{2}$

$\rm \: 25 = 9 + x {}^{2}$

$\rm \: 25 - 9 = x {}^{2}$

$\rm \: x {}^{2} = 16$

$\rm \: x = 4$

$\rm \: b \: = 4$

Some trigonometry ratio

$\rm \: \tan(A) = \frac{p}{b} = \frac{3}{4}$

$\rm \: \cos(A) = \frac{b}{h} = \frac{4}{5}$

We have to prove

$\rm \: \tan(A) + \frac{1}{ \cos(A) } = 2 \: \: or \: \: - 2$

$\rm \: \frac{3}{4} + \frac{1}{ \frac{4}{5} } = 2$

$\rm \frac{3}{4} + \frac{5}{4} = 2$

$\rm \: \frac{8}{4} = 2$

$\rm \: 2 = 2$

Hence proved