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Trigonometric Ratios of Compound Angles

Evaluate: 6...

Question

Evaluate:
$csc (65^{o} + 0) - sec (25^{o} - 0) - t a n (55^{o} + 0) + cot (35^{o} - 0)$ ?

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Solution

$C o s e c (65 + θ) - sec (25 - θ) - tan (55 - θ) + cot (35 + θ)$

$= sec [90 - (65 + θ)] - sec (25 - θ) - cot [90 - (55 - θ)] + cot (35 + θ)$
$s i n c e sec (90 - x) = c o s e c x, cot (90 - x) = t a n x$

$= sec (25 - θ) - sec (25 - θ) - cot (35 + θ) + cot (35 + θ)$

$= 0$

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Q. The value of

{sin}^{2} 65^{o} + {sin}^{2} 25^{o} + {cos}^{2} 35^{o} + {cos}^{2} 55^{o}

tan (55^{o} - A) - cot (35^{o} + A)

\frac{{sec}^{2} (90^{o} - θ) - {cot}^{2} θ}{2 ({sin}^{2} 25^{o} + {sin}^{2} 65^{o})} + \frac{2 {cos}^{2} 60^{o} {tan}^{2} 28^{o} {tan}^{2} 62^{o}}{sin 30^{o} cos 60^{o}}

\frac{c o s e c^{2} 63^{o} + {tan}^{2} 24^{o}}{{cot}^{2} 66^{o} + {sec}^{2} 27^{o}} + \frac{{sin}^{2} 63^{o} + {cos}^{2} 63^{o} sin 27^{o} + sin 27^{o} sec 63^{o}}{2 (c o {sec}^{2} 65^{o} - {tan}^{2} 25^{o})}

{sec}^{2} 60^{0} + sec 0^{0}

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