Question

Without using tables calculate :

${\bold{\sf{\frac{sin 25°}{sec 65°} \: + \: \frac{cos 25°}{cosec 65°}}}}$
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Answer 1

Step-by-step explanation:

Question :-

${\bold{\red{❒ \: \: \: \: \: }}}{\bold{\sf{Without \: using \: tables \: calculate : \: \frac{sin \: 25°}{sec \: 65°} \: + \: \frac{cos \: 25°}{cosec \: 65°}}}}$

Solution :-

${\bold{\sf{⟼ \: \: \: \: \: \frac{sin \: 25°}{sec \: 65°} \: + \: \frac{cos \: 25°}{cosec \: 65°}}}}$

${\bold{\sf{⟼ \: \: \: \: \: sin \: 25° \: cos \: 65° \: + \: cos \: 25° \: sin \: 65°}}}$

${\bold{\sf{⟼ \: \: \: \: \: sin \: 25° cos (90° \: - \: 25°) \: + \: cos \: 25° sin (90° \: - \: 25°)}}}$

${\bold{\sf{⟼ \: \: \: \: \: sin \: 25° \: sin \: 25° \: + \: cos \: 25° \: cos \: 25°}}}$

${\bold{\sf{⟼ \: \: \: \: \: sin² \: 25° \: + \: cos² \: 25° \: = \: 1}}}$