Question

if 5tanA=5, show that 5sinA-3cosA/5sinA+2casA =1/6​

Answer 1

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Answer 2

Question:-

If 5tanA=4, show that :-

5sinA - 3cosA / 5sinA + 2casA = 1/6

Solution:-

Given

$5 \tan \: a = 4$

$\tan(a) = \frac{4}{5}$

We know that

$\tan(a) = \frac{ \sin(a) }{ \cos(a) }$

Therefore,

$\frac{ \sin(a) }{ \cos(a) } = \frac{4}{5}$

$\sin(a) = 4$

$\cos(a) = 5$

Substitute these values in LHS

$\frac{5 \sin(a) - 3 \cos(a) }{5 \sin(a) + 2 \cos(a) }$

$\frac{(5 \times 4) - (3 \times 5)}{(5 \times 4) + (2 \times 5)}$

$\frac{20 - 15}{20 + 10}$

$= \frac{5}{30}$

$= \frac{1}{6}$

LHS = RHS

Hence, Proved