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Principal Solution of Trigonometric Equation

cos 58∘ cos 3...

Question

$c o s 58^{\circ} c o s 32^{\circ} - c o s 58^{\circ} s i n 58^{\circ}$

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Solution

$c o s 58^{\circ} c o s 32^{\circ} - c o s 58^{\circ} s i n 58^{\circ}$
= $c o s 58^{\circ} c o s (90 - 58)^{\circ} - c o s 58^{\circ} s i n 58^{\circ}$
= $c o s 58^{\circ} s i n 58^{\circ} - c o s 58^{\circ} s i n 58^{\circ}$
= $0$

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Q. Prove that (sin 32° cos 58° + cos 32° sin 58°) = 1.

\frac{cos 32^{\circ} sin 58^{\circ} + sin 32^{\circ} cos 58^{\circ}}{{c o t}^{2} 20^{\circ} + {tan}^{2} 70^{\circ}}

\frac{{sin 58}^{\circ}}{{cos 32}^{\circ}} + \frac{{tan 42}^{\circ}}{{cot 48}^{\circ}}

1 + c o s 56^{\circ} + c o s 58^{\circ} - c o s 66^{\circ} =

\frac{{c o s 58}^{\circ}}{{s i n 32}^{\circ}} + \frac{{s i n 22}^{\circ}}{{c o s 68}^{\circ}}

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Principal Solution of Trigonometric Equation

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