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If $tan A = 34$ , find the value of $1 sin A + 1 cos A$ .

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354

134

3512

34

answer is C.

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Detailed Solution

sin θ = Opposite side Hypotenuse cos θ = Adjacent side Hypotenuse tan θ = Opposite side Adjacent side

Find the value of

B C A B

Given that,

tan A = 34

.
Which implies,

Side opposite to angle A Side opposite to angle A = 34

Consider triangle ABC.
Question Image

\Rightarrow

tan A = B C A B = 34

Let us assume BC = 3x and AB = 4x.
Applying Pythagoras Theorem,

(A C) 2 = (B C) 2 + (A B) 2 (A C) 2 = (3 x) 2 + (4 x) 2 (A C) 2 = 9 x 2 + 16 x 2 (A C) 2 = 25 x 2 A C = 25 x 2 A C = 5 x

Now,

sin A = Side opposite to angle A Hypoten  Use

sin A = B C A C

sin A = 3 x 5 x

sin A = 35

Similarly,

cos A = Side adjacent A Hypotenuse cos A = A B A C cos A = 4 x 5 x cos A = 45

As we have the required values, let us find the value of

1 sin A + 1 cos A

1 sin A + 1 cos A = 135 + 145 = 53 + 54 = 5 × 4 + 5 × 3 3 × 4 = 20 + 15 12 = 3512

Therefore, the value of

1 sin A + 1 cos A = 3512

.
The correct option is (3).

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