Question

SHOW that: (sin35/cos55) -2cos^60=1/2​

Answer 1

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Answer 2

$LHS = \big(\frac{sin\:35\degree }{cos\:55\degree }\big)^{2} - 2 cos^{2} \:60\degree$

$= \big(\frac{sin\:35\degree }{cos\:(90 - 35\degree) }\big)^{2} - 2 cos^{2} \:60\degree$

$=\big(\frac{sin\:35\degree }{sin\:35\degree }\big)^{2} - 2 cos^{2} \:60\degree$

$= 1^{2} - 2 \times \big(\frac{1}{2}\big)^{2} \\= 1 - 2 \times \frac{1}{4} \\= 1 - \frac{1}{2} \\= \frac{1}{2} \\= RHS$

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