Question

If $tan^{2}45^{0}-cos^{2}30^{0}=xsin45^{0}cos45^{0}$, then x =
(a)2
(b)−2
(c)$\frac{-1}{2}$
(d)$\frac{1}{2}$

Answer 1

SOLUTION :  

The correct option is (d) : 1/2

Given : tan² 45° - cos ² 30° = x sin 45° cos 45°  

tan² 45° - cos ² 30° = x sin 45° cos 45°  

= 1² - (√3/2)² = x (1/√2) (1/√2)

[tan 45° = 1 , cos 30° = √3/2 ,  sin 45° =  cos 45° = 1/√2]

= 1 - ¾ = x × ½

= (4 - 3)/4 = x/2

= ¼ = x/2  

= 4x  = 2

= x = 2/4 = ½  

= x = ½  

Hence, the value of x is ½ .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

option(d)

Step-by-step explanation:

Trigonometry values:

(i) sin45° = (1/√2)

(ii) cos45° = (1/√2)

(iii) tan45 = 1

(iv) cos30 = (√3/2)

Now,

Given Equation is tan²45° - cos²30 = xsin45°cos45°

⇒(1)² - (√3/2)² = x(1/√2)(1/√2)

⇒ 1 - (3/4) = x(1/2)

⇒ (1/4) = x/2

⇒ 2 = 4x

⇒ x = 2/4

⇒ x = 1/2.

Therefore, the value of x = 1/2.

Hope it helps!