Question

$\huge\underline{\bf \orange{Question :}}$

sin A + cos A / sec A + cosec A = sin A . cosA​

Answer 1

Answer:

$\huge{\underline{\mathtt{\red{❥A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$(sinA+cosA)(secA+cosecA)=(sinA+cosA)∗(1cosA+1sinA)

=(sinA+cosA)sinA+cosAsinAcosA

=(sinA+cosA)2sinAcosA

=sin2A+2sinAcosA+cos2AsinAcosA=1+2sinAcosAsinAcosA

=1sinAcosA+2sinAcosAsinAcosA

=cosecAsecA+2

Answer 2

Step-by-step explanation:

LHS

sin A +cos A/sec A + cosec A

=sin A +(cos A)/1/cos A +1/sin A

=sin A+ cos A×cos A+ 1/sin A

=sin A+ cos^2 A+ 1/sin A

taking LCM

=(sin^2 A+ cos^2 A +1)/sin A