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f(x)=2\sin^2{x}+ \cos^{4}{x}-3 \ \ \ \ \ \ x\epsilon R

Find out the no. of solutions for f(x)=0

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

\infty


Answers (1)

best_answer

 

Trigonometric Functions of Acute Angles -

 

Trigonometric Functions of Acute Angles-

We can define the trigonometric functions in terms of an angle t and the lengths of the sides of the triangle. The adjacent side is the side closest to the angle, x. (Adjacent means “next to.”) The opposite side is the side across from the angle, y. The hypotenuse is the side of the triangle opposite the right angle, 1. 

       


 

\\\mathrm{Sine\;\;\;\;\sin t=\frac{\text { opposite }}{\text { hypotenuse }}}\\\mathrm{Cosine\;\;\;\;\cos t=\frac{\text { adjacent }}{\text { hypotenuse }}}\\\mathrm{Tangent\;\;\;\;\tan t=\frac{\text { opposite }}{\text { adjacent }}}

 

Reciprocal Function

In addition to sine, cosine, and tangent, there are three more functions. These too are defined in terms of the sides of the triangle.\\\mathrm{Cosecant\;\;\;\;\csc t=\frac{\text { hypotenuse }}{\text { opposite }}=\frac{1}{\sin t}}\\\mathrm{Secent\;\;\;\;\sec t=\frac{\text { hypotenuse }}{\text { adjacent }}=\frac{1}{\cos t}}\\\mathrm{Cotangent\;\;\;\;\cot t=\frac{\text { adjacent }}{\text { opposite }}=\frac{1}{\tan t}}

 

Since, the hypotenuse is the greatest side in a right angle triangle, \text{sint} and \text{cost } can never be greater than unity and \text{cosect} and \text{sect} can never by less than unity. 

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f(x)=2\sin^2{x}+ \cos^{4}{x}-3=0 \ \ \ \ \ \ x\epsilon R \\ 2\sin^2{x}+ \cos^{4}{x}=3 \\ L.H.S< 3 \ for\ every\ x

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Anam Khan

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