Question

If SecA + TanA = 3 Find sinA + cos A​

Answer 1

ANSWER.......................

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Answer 2

Given: Sec A + Tan A = 3

To find: The value of sin A + cos A​

Solution:

• Now we have given that sec A + tan A = 3

• Converting it to sin and cos, we get:

              1 / cos A + sin A / cos A = 3

              1 + sin A = 3 cos A

• Now squaring on both the sides, we get:

              ( 1 + sin A )^2 = 9 cos^2 A

              1 + sin^2 A + 2 sin A = 9 ( 1 - sin^2 A )

              1 + sin^2 A + 2 sin A = 9 - 9 sin^2 A

              9 sin^2 A + sin^2 A + 2 sin A = 9 - 1

              10 sin^2 A + 2 sin A - 8 = 0

              10 sin^2 A + 10 sin A - 8 sin A - 8 = 0

              10 sin A (sin A + 1) - 8 (sin A + 1) = 0

              (10 sin A - 8) (sin A + 1) = 0

              sin A = 4/5 or -1

• If sin A = -1

              A = -π/2

• Now we have sec A = 1/ cos A = 1/(cos(-π/2)) = 1/ 0 = undefined.

• So consider sin A = 4/5

• Then cos A = 3/5 ..................(by pythagoras theorem)

• So sin A + cos A​ = 4/5 + 3/5 = 7/5

Answer:

         So the value of sin A + cos A is 7/5.