Question

3tanthetha+cotthetha=5cosecthetha find the value of thetha​

Answer 1

Answer:

3tanα+cotα=5cosecα

3sinα/cosα+cosα/sinα=5/sinα

3sin^2α+cos^2α/cosαsinα=5/sinα

3sin^2α+cos^α=5cosα

3(1-cos^2α)+cos^α=5cosα

2cos^2α+5cosα-3=0

2cos^2α+6cosα-cosα-3=0

2cosα(cosα+3)-1(cosα+3)=0

(2cosα-1)(cosα+3)=0

2cosα=1 or cosα=-3

as cosα will never be <-1

cosα=1/2

α=π/3