Question

Prove that 1+seca+tana=2/1+cota-coseca

Answer 1

L.H.S = ( 1+ cota-coseca) ( 1+ tana -seca)
Step-by-step explanation:
= (1+cosa/sina-1/sina) (1+sina/cosa-1/cosa)
= (sina+cosa-1/sina) (cosa+sina-1/cosa)
= ((sina+cosa) - (1)/sina) ((cosa+sina) - (1)/cosa)
= ((sina+cosa)raise to power2 - (1)raise to power 2)/sinacosa
= sin2a+cos2a+2sinacosa-1/sinacosa
= 1+2sinacosa-1/sinacosa (because sin2a+cos2a=1)
= 2sinacosa/sinacosa
=2
=R.H.S

Answer 2

$(1 + seca + tana)(1 + cota - coseca) \\ \\ = ( \frac{cosa + 1 + sina}{cosa} )( \frac{sina + cosa - 1}{sina} ) \\ \\ = \frac{( {cosa + sina})^{2} - 1 }{sinacosa} \\ \\ = \frac{2sinacosa}{sinacosa} \\ \\ = 2$