Question

if 3sin (theta) +4 cos (theta) =5 then find the value of sin theta

Answer 1

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Answer 2

$sin\theta=\dfrac{3}{5}$

Step-by-step explanation:

Here, $3\:sin\theta+4\:cos\theta=5$

$\Rightarrow 4\:cos\theta=5-3\:sin\theta$

Now, squaring both sides, we get

$(4\:cos\theta)^{2}=(5-3\:sin\theta)^{2}$

$\Rightarrow 16\:cos^{2}\theta=25-30\:sin\theta+9\:sin^{2}\theta$

$\Rightarrow 16-16\:sin^{2}\theta=25-30\:sin\theta+9\:sin^{2}\theta$

• since $sin^{2}\theta+cos^{2}\theta=1$

$\Rightarrow 25\:sin^{2}\theta-30\:sin\theta+9=0$

$\Rightarrow (5\:sin\theta-3)^{2}=0$

$\Rightarrow 5\:sin\theta-3=0$

$\Rightarrow 5\:sin\theta=3$

$\Rightarrow sin\theta=\dfrac{3}{5}$

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