Question

If 4 cos^2θ + 4 sinθ - 5 = 0, show that sin θ = 1/2. anyone to solve this how to solve it ​

Answer 1

Step-by-step explanation:

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$\mathtt{\large{\purple{\underline{\underline{given}}}}} \\ \\ \displaystyle \sf \longrightarrow \: 4 \cos^{2} ( \theta) + 4 \sin( \theta) - 5 = 0 \\ \\ \mathtt{\large{\red{\underline{\underline{solution}}}}} \\ \\ \displaystyle \sf \longrightarrow 4(1 - \sin ^{2} ( \theta) ) + 4 \sin( \theta) - 5 = 0 \\ \\ \displaystyle \sf \longrightarrow 4 - 4 \sin ^{2} ( \theta) + 4 \sin( \theta) - 5 = 0 \\ \\ \displaystyle \sf \longrightarrow - 4 \sin ^{2} ( \theta) + 4 \sin( \theta) - 1 = 0 \\ \\ \displaystyle \sf \longrightarrow - (4 \sin ^{2} ( \theta) - 4 \sin( \theta) + 1) = 0 \\ \\ \displaystyle \sf \longrightarrow 4 \sin ^{2} ( \theta) - 2 \sin( \theta) - 2 \sin( \theta) + 1 = 0 \\ \\ \displaystyle \sf \longrightarrow \: 2 \sin( \theta) (2 \sin( \theta - 1) - 1(2 \sin( \theta - 1) = 0 \\ \\\displaystyle \sf \longrightarrow(2 \sin \theta - 1) ( 2 \sin( \theta - 1) = 0 \\ \\ \displaystyle \sf \longrightarrow \: \sin( \theta) = \frac{1}{2} \\ \\ \\ \sf \huge hence \: proved$