Question

if cosectheta + cot theta =5 evaluate sectheta

Answer 1

Step-by-step explanation:

1/sinø+cosø/sinø=5

1+cosø=5sinø

(1+cosø)²=5² sin²ø

(1+cosø)(1+cosø)=25(1-cos²ø)

(1+cosø)(1+cosø)=25(1+cosø)(1-cosø)

(1+cosø)=25(1-cosø)

1+cosø=25-25cosø

cosø+25cosø=25-1

cosø(25+1)=24

cosø=24/26

note: secø=1/cosø

taking inverse on both sides we get

1/cosø=1/24/25

secø=25/24