Maths / Introduction to Trigonometry / Trigonometric Ratios

QUESTION
 

For  large tantheta =frac{1}{2}, arrange the values of large (1+Sin^2theta),(Cos^2theta-Sin^2theta);and;(2Sintheta.costheta) in ascending order.

EXPLANATION
Explain TypeExplanation Content
Text

tan theta=frac{1}{2}

Let ABC be a right triangle and angle C be theta.

Then, AB = x

BC = 2x

AC=sqrt{5}X

Now, sin theta=frac{1}{sqrt{5}},costheta=frac{2}{sqrt{5}}

Now,  1 +sin^2theta=1+left ( frac{1}{sqrt{5}} right )^2=1+frac{1}{5}=frac{6}{5}

cos^2theta-sin^2theta=frac{4}{5}-frac{1}{5}=frac{3}{5}

2 sintheta cos theta =2times frac{1}{sqrt{5}}times frac{2}{sqrt{5}}=frac{4}{5}

Ascending order: frac{3}{5},frac{4}{5},frac{6}{5}

rightarrow   (cos^2 theta-sin^2 theta)(2sintheta costheta),(1+sin^2 theta)

 

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