Question

if secant theta minus tan theta is equal to 4 find the value of cos theta​

Answer 1

Answer:

Given: sec∅- tan ∅=4

To find: cos∅

Solution: sec∅-tan∅=4 ....(i)

multiplying and dividing by sec∅+tan∅

sec∅-tan∅ ×sec∅+tan∅/sec∅+tan∅=4

sec²∅- tan²∅/ sec∅+tan∅=4

As sec²∅-tan²∅=1. So,

1/sec∅+tan∅=4

sec∅+tan∅=1/4 ......(ii)

Adding equation (i) and (ii)

sec∅+tan∅=1/4

sec∅-tan∅=4

= 2sec∅=17/4

= sec∅= 17/8

→. cos∅ = 1/(17/8)

→ cos∅ = 8/17

HENCE PROVED !