Question

sinA(1+tanA)+cosA(1+cotA)=secA+tanA​

Answer 1

Answer:

proved

Step-by-step explanation:

sina(1+tana)+cosa(1+cota)

$sina(1 + \frac{sina}{cosa} ) + cosa(1 + \frac{cosa}{sina} ) \\ = sina( \frac{sina + cosa}{cosa} ) + cosa( \frac{sina + cosa}{sina} ) \\ = (sina + cosa)( \frac{sina}{cosa} + \frac{cosa}{sina} ) \\ = (sina + cosa)( \frac{sin {}^{2}a + cos {}^{2} a }{sina \: cosa} ) \\ = (sina + cosa)( \frac{1}{sina \: cosa} ) \\ = ( \frac{sina}{sina \: cosa} + \frac{cosa}{sina \: cosa} ) \\ = ( \frac{1}{cosa} + \frac{1}{sina} ) \\ = sec \: a \: + \: cosec \: a$