Question

WILL MARK AS BRAINLIEST If tan2 45° − cos2 30° = x cos 45° sin 45°, then find x.

Answer 1

Answer:

(-1)

Step-by-step explanation:

substitution of the values

1-3/4 - 3/4 = x(1/2)

-2/4 = x (1/2)

-1/2 = x(1/2)

therefore x = -1

Answer 2

Answer:

$\large\boxed{\star\:\:x=\frac{1}{2}\:\:\star}$

Step-by-step explanation:

$\large\star$Given:-

 Tan²45°- Cos²45°= x ×Cos 45°×Sin 45°

$\large\star$To Find:-

 The Value of x.

$\large\star$According to the Trigonometry Table:-

 tan 45°=1, cos 30°=$\frac{\sqrt{3} }{2}$, cos 45°=sin 45°=$\frac{1}{\sqrt{2} }$.

$\large\star$Solution:-

  Tan²45°- Cos²45°= x ×Cos 45°×Sin 45°

⇒$(1)^2-(\frac{\sqrt{3} }{2} )^2=x\times\frac{1}{\sqrt{2} } \times\frac{1}{\sqrt{2} }$

⇒$1-\frac{3}{4}=x\times\frac{1}{\sqrt{2} } ^2$

⇒$\frac{4-3}{4}=x\times\frac{1}{2}$

⇒$\frac{1}{4}=x\times\frac{1}{2}$

Cross Multiplying $\frac{1}{2}$:-

⇒$\frac{2}{4}=x$

$\implies\large\boxed{x=\frac{1}{2}}$