Question

# ; then the general solution of A=

Hint:

### A general solution is one which involves the integer ‘n’ and gives all solutions of a trigonometric equation.

## The correct answer is:

### We have, tan(π/4 + A/2) + tan (π/4 - A/2) = 4/√3

=> (1+ tanA/2)/(1-tanA/2) + (1-tanA/2)/(1+tanA/2) = 4/√3

=> {(1 + tan²A/2 + 2tanA/2) + (1 + tan²A/2 - 2tanA/2)}/ (1- tan²A/2) = 4/√3

=> {2(1+ tan²A/2)}/(1 - tan²A/2) = 4/√3

=> (1-tan²A/2)/(1+tan²A/2) = √3/2

=> cos 2(A/2) = cos π/6

=> cosA = cos π/6

=> A = 2nπ ± π/6.

Hence, the correct option is C.

tan (π/4 + A) = (1+tanA)/(1-tanA).

### Related Questions to study

Three forces , and act on an object simultaneously. These force vectors are shown in the following free-body diagram. In which direction does the object accelerate?

Three forces , and act on an object simultaneously. These force vectors are shown in the following free-body diagram. In which direction does the object accelerate?

### The general solution of is

### The general solution of is

### If then x = - ....

11 sin

^{2}x + 7 cos

^{2}x = 8 .

Or, 11 sin

^{2}x + 7 ( 1 - sin

^{2}x) = 8 .

Or, 11 sin

^{2}x + 7 - 7sin

^{2}x = 8 .

Or, 11sin

^{2}x - 7 sin

^{2}x = 8 - 7 .

Or, 4sin

^{2}x = 1

Or, sin

^{2}x = 1/4

Or, Sin

^{2 }x= Sin

^{2 }π/6

x = π/6

Hence, the correct option is (c).

### If then x = - ....

11 sin

^{2}x + 7 cos

^{2}x = 8 .

Or, 11 sin

^{2}x + 7 ( 1 - sin

^{2}x) = 8 .

Or, 11 sin

^{2}x + 7 - 7sin

^{2}x = 8 .

Or, 11sin

^{2}x - 7 sin

^{2}x = 8 - 7 .

Or, 4sin

^{2}x = 1

Or, sin

^{2}x = 1/4

Or, Sin

^{2 }x= Sin

^{2 }π/6

x = π/6

Hence, the correct option is (c).

### The general solution of i

Tan 2x - Tan x / 1 + Tan x. Tan 2x = 1 .

Or, Tan (2x - 1 ) = 1 .

Or, Tan x = 1 .

Hence, the correct option is (d).

### The general solution of i

Tan 2x - Tan x / 1 + Tan x. Tan 2x = 1 .

Or, Tan (2x - 1 ) = 1 .

Or, Tan x = 1 .

Hence, the correct option is (d).

### If then

then = 0

### If then

then = 0

### The most general value of satisfying the equations is

### The most general value of satisfying the equations is

### The smallest value of satisfying the equation IS

### The smallest value of satisfying the equation IS

### If and is acute then

### If and is acute then

### If then x=

### If then x=

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I) The weight of the 5 kg mass acts vertically downwards

II) The net vertical force acting on the body is 30 N.

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II) The net vertical force acting on the body is 30 N.

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