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MHTCET 20 Apr 2026 Shift 2 Paper

Question : 104 of 150

Marks: +1, -0

x+y=\frac{\pi}{4}

(1+\tan x)(1+\tan y)=

Solution:

Concept:

Use the tangent addition formula and then expand the required product.

Explanation:

Given

x+y=\frac{\pi}{4}

, take tangent on both sides.

\tan(x+y)=\tan\frac{\pi}{4}=1

Using the formula

\tan(x+y)=\frac{\tan x+\tan y}{1-\tan x\tan y}

, we get:

\frac{\tan x+\tan y}{1-\tan x\tan y}=1

Cross-multiplying:

\tan x+\tan y=1-\tan x\tan y

Rearranging:

\tan x+\tan y+\tan x\tan y=1

Now expand the required expression:

(1+\tan x)(1+\tan y)=1+\tan x+\tan y+\tan x\tan y

Substitute the known value:

(1+\tan x)(1+\tan y)=1+1=2

Answer:

The correct answer is

2

, which is option B.

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