Prove that:
$$
2 \sin ^{2} \frac{\pi}{6}+\operatorname{cosec}^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}
$$

Answer

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Video Transcript

and discussion. We have to prove that two times signing square 5.6 plus CO six square 75 upon six times go square 5.3 equal to three upon to. So here we take the left hand side and we simplify this. So here two times sign square 5.6 plus CO six square bye plus 5.6. Because here we know that bye plus 5.6 equal to seven by upon six. So now I put here populist 5.6 times go square five on three. So now two times sign square 5.6 plus. Now here we know that go see five plus tita equal to You can see that it is, it is in third quarter and so it will be negative. Cool. See Tito. So now we apply here so we get negative. Cool. See 5.6 to the power to times. Cool. Square 5.3. Now here we know that the value of signed pipe on six value is one upon too. So we put here two times 1.2 to the power to positive cause a 5.6 value is too. So we put here negative two to the power to times goes by upon three value is one upon to. So now we simplify this and here we get one up on two plus one equal to three upon to. So here you can see that two times sine squared five on six plus koszics choir 75 on six times Gold square by upon three value is three upon to. So here left hand side equal to right inside. So here we can say hands screwed so it is over final answer.

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