Question

if sec theta-tan theta = 4 then find the value of cosec theta

Answer 1

sec theta - tan theta = 4-----(1)
or, (sec theta - tah theta) (sec theta + tan theta) = 4(sec theta - tan theta)
or,sec²theta - tan²theta = 4(sec theta - tan theta)
or, 1 = 4(sec theta - tan theta)
sec theta + tan theta = 1/4------(2)

Now (1) + (2)
sec theta-tan theta = 4
sec theta + tan theta = 1/4

or, 2sec theta = 4+1/4
or, 2sec theta = 17/4
or, sec theta = 17/8
so, tan theta = 1/4 - 17/8
or, tan theta = -15/8
or, sin theta = -15/17
so,cosec theta = 1/sin theta
cosec theta = -17/15

Hope it'll help you :)