Question

tan 50 + cot 40. = ?
​

Answer 1

Answer:

2tan 50 or 2cot 40

Step-by-step explanation:

tan 50 + tan (90-40)

= 2tan 50

Answer 2

tan 50° + cot 40° = 2 tan 50°

Correct question : tan 50° + cot 40° = (A) 1 (B) cot 40° (C) tan 50° (D) 2 tan 50°

Given :

tan 50° + cot 40°

To find :

tan 50° + cot 40° =

(A) 1

(B) cot 40°

(C) tan 50°

(D) 2 tan 50°

Formula Used :

cot (90° - θ) = tan θ

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

tan 50° + cot 40°

Step 2 of 2 :

Choose the correct option

We are aware of the trigonometric identity that

cot (90° - θ) = tan θ

Thus we get

tan 50° + cot 40°

= tan 50° + cot (90 ° - 50°)

= tan50° + tan50° [ ∵ cot (90° - θ) = tan θ]

= 2 tan 50°

Hence the correct option is (D) 2 tan 50°

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