Math, asked by dghtddby, 9 months ago

Rationalise sina + cosa/sina - cosa

Answers

Answered by Anonymous

2

Answer:

cosA−sinA+1cosA+sinA−1

=(cosA−sinA+1)(cosA+sinA+1)(cosA+sinA−1)(cosA+sinA+1)

=(cosA+1¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−sinA)(cosA+1¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+sinA)(cosA+sinA¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−1)(cosA+sinA¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+1)

=(cosA+1)2−(sinA)2(cosA+sinA)2−12

=cos2A+2cosA+1−sin2Acos2A+sin2A+2sinAcosA−1

=cos2A+2cosA+cos2A1+2sinAcosA−1(∵ cos2A+sin2A=1)

=2cos2A+2cosA2sinAcosA

=2cos2A2sinAcosA+2cosA2sinAcosA

=cosAsinA+1sinA

=cotA+cosecA

=cosecA+cotA

Proved.

Step-by-step explanation:

Mark as brainlist please

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