If 5 tan = 4, then Class 10 Maths Introduction to Trigonometry questions with solutions

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Solution

Q.
If 5 tanβ = 4, then $\frac{5 \sin β - 2 \cos β}{5 \sin β + 2 \cos β} =$

1 1/3

2 2/5

3 3/5

4 6

Ans.
(1)

$5 \tan β = 4 \Rightarrow \tan β = \frac{4}{5}$

$∴$ $\frac{5 \sin β - 2 \cos β}{5 \sin β + 2 \cos β} = \frac{5 \tan β - 2}{5 \tan β + 2}$ $[dividing \cos β by Nr. and Dr.]$

$= \frac{5 \times \frac{4}{5} - 2}{5 \times \frac{4}{5} + 2} = \frac{2}{6} = \frac{1}{3}$

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