Question

If sectheta+ tantheta =5 then sectheta - tantheta =​

Answer 1

Answer:

convert the background

Answer 2

Given:

sec∅+ tan∅ =5

To find:

sec∅ - tan∅

Solution:

We know,

a²- b² = (a+b)×(a-b)...(1)

and, sec²∅ - tan²∅ = 1 ....(2)

We have,

sec∅ + tan∅ = 5

now, multiplying sec∅ - tan∅ on both the sides, we get

(sec∅ + tan∅) × (sec∅ - tan∅) = 5(sec∅ - tan∅)

applying the rule in equation 1 we get,

sec²∅ - tan²∅ = 5(sec∅ - tan∅)

using the value of sec²∅ - tan²∅  from equation 2.

⇒ 1 = 5(sec∅ - tan∅)

⇒ $\frac{1}{5}$ = sec∅ - tan∅

Hence the value of sec∅ - tan∅ is $\frac{1}{5}$.