Question

cot (15° - A) + tan(15° + A) =

a) 4cos2A/1 + 2cos2A
b) 4cos2A/1 - 2sin2A
c)4cos2A/1 + 2sin2A
d) 4cos2A/1 - 2cos2A
​

Answer 1

☑REFER THE ATTACHMENT ☑

➵HENCE OPTION B IS CORRECT☑

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cot (15° - A) + tan(15° + A) =?

ANSWER-:

$4cos2A/ 1-2sinA$

Answer 2

EXPLANATION.

⇒ cot(15° - A) + tan(15° + A).

As we know that,

We can write equation as,

⇒ cot(15° - A) = cos(15° - A)/sin(15° - A).

⇒ tan(15° + A) = sin(15° + A)/cos(15° + A).

Using this formula in equation, we get.

⇒ cos(15° - A)/sin(15° - A) + sin(15° + A)/cos(15° + A).

Taking L.C.M. in equation, we get.

⇒ cos(15° - A).cos(15° + A) + sin(15° + A).sin(15° - A)/sin(15° - A).cos(15° + A).

As we know that,

Formula of :

⇒ cos(A - B) = cos(A).cos(B) + sin(A).sin(B).

Using the formula in equation, we get.

⇒ cos[(15° - A) - (15° + A)]/sin(15° - A).cos(15° + A)

⇒ cos[15° - A - 15° - A]/sin(15° - A).cos(15° + A).

⇒ cos[-2A]/sin(15° - A).cos(15° + A).

Multiply and divide the equation by 2, we get.

⇒ 2 cos(-2A)/2sin(15° - A).cos(15° + A).

As we know that,

Formula of :

⇒ 2 cos(A).sin(B) = sin(A + B) - sin(A - B).

Using this formula in equation, we get.

⇒ 2 cos(-2A)/sin[(15° - A) + (15° + A)] - sin[(15° - A) - (15° + A)].

⇒ 2 cos(-2A)/sin[15° - A + 15° + A] - sin[15° - A - 15° - A].

⇒ 2 cos(-2A)/sin(30°) - sin(-2A).

As we know that,

Formula of :

⇒ sin30° = 1/2.

Using this formula in equation, we get.

⇒ 2 cos(-2A)/1/2 - sin(-2A).

⇒ 2 cos(-2A)/1 - 2 sin(-2A)/2.

⇒ 4 cos(-2A)/1 - 2 sin(-2A).

⇒ 4 cos(2A)/1 - 2 sin(2A).

Hence, option [B] is correct answer.

                                                                                                                     

MORE INFORMATION.

Fundamental trigonometric identities.

(1) = sin²θ + cos²θ = 1.

(2) = 1 + tan²θ = sec²θ.

(3) = 1 + cot²θ = cosec²θ.