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Sign of Trigonometric Ratios in Different Quadrants

Prove that ...

Question

Prove that $sin 55^{o} + cos 25^{o} = 2 cos 55^{o}$

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Solution

$s i n 55^{\circ} + c o s 25^{\circ}$
$\Rightarrow s i n (90^{\circ} - 25^{\circ}) + c o s 25^{\circ}$
$\Rightarrow c o s 25^{\circ} + c o s 25^{\circ} = 2 c o s 25^{\circ}$

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Q. Prove the following:

sin (25^{O} + θ) \cdot cos (25^{o} - ϕ) - cos (25^{o} + θ) \cdot sin (25^{o} - ϕ) = sin (θ + ϕ)

\frac{cos 25^{o} + sin 25^{o}}{cos 25^{o} - sin 25^{o}}

=

\frac{sin 65^{o}}{cos 25^{o}}

Q. The value of

\frac{cot 40^{o}}{tan 50^{o}} - \frac{1}{2} (\frac{cos 35^{o}}{sin 55^{o}})

\frac{sin 65^{o}}{cos 25^{o}} + \frac{cos 32^{o}}{sin 58^{o}} - sin 28^{o} sec 62^{o} + {cosec}^{2} 30^{o}

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Sign of Trigonometric Ratios in Different Quadrants

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