Question

50. यदि 4cose+3sine = 5, तब tane का मान ज्ञात करें।​

Answer 1

Question :-

• If 4 cose + 3 sine = 5, find the value of tane.

Answer :-

Given :-

• 4 cose + 3 sine = 5

To find :

• Value of tane

Formula used :-

• sin(x + y) = sinx cosy + siny cosx
• tan(90° - x) = cotx

Solution :-

4 cose + 3 cose = 5

Divide both sides by 5, we get

$\bf\implies \:\dfrac{4}{5} cose+ \dfrac{3}{5} sine = 1$

$\bf\implies \:Let\dfrac{4}{5} = sinx \: and \: \dfrac{3}{5} = cosx$

$\bf\implies \:sinx \: cose + sine \: cosx = 1$

$\bf\implies \:sin(x + e) = sin90$

$\bf\implies \:x + e = 90$

$\bf\implies \:e = 90 - x$

$\bf\implies \:tane = tan(90 - x) = cotx$

$\bf\implies \:cotx = \dfrac{cosx}{sinx} = \dfrac{\dfrac{3}{5} }{\dfrac{4}{5} } = \dfrac{3}{4}$

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$\bf\implies \:tane = \dfrac{3}{4}$