Question

If tan² 45° - cos² 60° - x sin 45° . tan 60° = 0 then x = *

Answer 1

Answer:

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Explanation:

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Answer 2

Step by step explanation:

Given : An expression $tan^{2} 45\°-cos^{2} 60\°-x*sin45\°*tan60\°=0$

To find : The value of x

Trigonometric values used : We use trigonometric values to solve the expression,

1. $tan 45\°=1$
2. $cos60\°=\frac{1}{2}$
3. $sin45\°=\frac{1}{\sqrt{2} }$
4. $tan60\°=\sqrt{3}$

• Calculation for x :

We have,

⇒  $tan^{2} 45\°-cos^{2} 60\°-x*sin45\°*tan60\°=0$

by putting all the required values of trigonometric functions in given expression we can find the value of x,

⇒  $(1)^{2} -(\frac{1}{2} )^{2} -x*\frac{1}{\sqrt{2} } *\sqrt{3} =0$

⇒  $1-\frac{1}{4} -x*\frac{\sqrt{3} }{\sqrt{2} }=0$

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

⇒  $\frac{3}{4} =\frac{\sqrt{3} }{\sqrt{2} } *x$

⇒  $x=\frac{3}{4} *\frac{\sqrt{2} }{\sqrt{3} }$

⇒  $x=\frac{\sqrt{3} }{2\sqrt{2} }$

we get the value of x is $x=\frac{\sqrt{3} }{2\sqrt{2} }$.