Question

find 1- sin2theta / 1 + cos theta​

Answer 1

EXPLANATION.

$\sf \: \implies \: 1 - \dfrac{ \sin {}^{2} ( \theta) }{1 + \cos( \theta) } \\ \\ \sf \: \implies \: 1 - \frac{1 - \cos {}^{2} ( \theta) }{1 + \cos( \theta) } \\ \\ \sf \: \implies \: \frac{1 + \cos( \theta) - (1 - \cos {}^{2} ( \theta)) }{1 + \cos( \theta) } \\ \\ \sf \: \implies \: \frac{1 + \cos( \theta) - 1 + \cos {}^{2} ( \theta) }{1 + \cos( \theta) }$

$\sf \: \implies \: \dfrac{ \cos( \theta) + \cos {}^{2} ( \theta) }{1 + \cos( \theta) } \\ \\ \sf \: \implies \: \frac{ \cos( \theta)(1 + \cos( \theta)) }{1 + \cos( \theta) } = \cos( \theta)$

More information.

Sin ø = P/h = perpendicular/hypotenuse.

cos ø = b/h = base/hypotenuse.

tan ø = p/b = perpendicular/base.

csc ø = h/p = hypotenuse/perpendicular.

sec ø = h/b = hypotenuse/base.

cot ø = b/p = base/perpendicular.

Sin²ø + cos²ø = 1.

tan²ø + 1 = sec²ø.

1 + cot²ø = csc²ø.