1.

(Cos A + sin A) ( tan A + cot A) = sec A + cosec AHow do I solve this?

Answer»

Step-by-step EXPLANATION:

(cosa + \sin(a) ( \tan(a) + \cot(a) ) \\ = ( \cos(a) + \sin(a) )( \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) } ) \\ = \cos(a) + \sin(a) \times \frac{ \sin(a) \times \sin(a) + \cos(a) \times \cos(a) }{ \sin(a) \times \cos(a) } \\ = \frac{ \cos(a) + \sin(a) }{ \sin(a) \times \cos(a) } \times { \sin(a) }^{2} + { \cos(a) }^{2} \\ = \frac{ \cos(a) }{ \sin(a) \times \cos(a) } + \frac{ \sin(a) }{ \sin(a) \times \cos(a) } \times 1 \\ = \frac{1}{ \sin(a) } + \frac{1}{ \cos(a) } \\ = \cosec(a) + \sec(a) \: \: \: \: \: r.h.s


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