Question

If tan² 45°-cos² 30°=x. sin 45° cos 45° ,then the value of x is

Answer 1

tan45 = 1

cos30 = root3/2

sin45= 1/root2=cos45

(1)^2-(3/4)=x. (1/root2)(1/root2)

1-3/4 =x/2

1/4=x/2

or x = 1/2

therefore x=cos60=sin30

Answer 2

The value of x is $x=\frac{1}{2}$.

Step-by-step explanation:

Given : Equation $\tan^2 45^\circ-\cos^2 30^\circ=x\cdot \sin 45^\circ\cos 45^\circ$

To find : The value of x ?

Solution :

Using trigonometric values,

$\sin 45^\circ=\frac{1}{\sqrt{2}}$

$\cos 30^\circ=\frac{\sqrt3}{2}$

$\cos 45^\circ=\frac{1}{\sqrt{2}}$

$\tan 45^\circ=1$

Substituting in equation,

$(1)^2-(\frac{\sqrt3}{2})^2=x\cdot (\frac{1}{\sqrt{2}})(\frac{1}{\sqrt{2}})$

$1-\frac{3}{4}=x\cdot \frac{1}{2}$

$\frac{4-3}{4}=x\cdot \frac{1}{2}$

$\frac{1}{4}=x\cdot \frac{1}{2}$

$x=\frac{2}{4}$

$x=\frac{1}{2}$

Therefore, the value of x is $x=\frac{1}{2}$.

#Learn more

Prove tan(45+a)+tan(45-a)/tan(45+a)-tan(45-a)=cosec2a

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