Maths / Introduction to Trigonometry / Trigonometric Ratios

QUESTION

For  $\dpi{120} \fn_jvn \large tan\theta =\frac{1}{2},$ arrange the values of $\dpi{120} \fn_jvn \large (1+Sin^2\theta),(Cos^2\theta-Sin^2\theta)\;and\;(2Sin\theta.cos\theta)$ in ascending order.

EXPLANATION
Explain TypeExplanation Content
Text

tan $\dpi{80} \fn_phv \theta=\frac{1}{2}$

Let ABC be a right triangle and $\dpi{80} \fn_phv \angle C$ be $\dpi{80} \fn_phv \theta$.

Then, AB = x

BC = 2x

$\dpi{80} \fn_phv AC=\sqrt{5}X$

Now, sin $\dpi{80} \fn_phv \theta=\frac{1}{\sqrt{5}},cos\theta=\frac{2}{\sqrt{5}}$

Now,  $\dpi{80} \fn_phv 1 +sin^2\theta=1+\left ( \frac{1}{\sqrt{5}} \right )^2=1+\frac{1}{5}=\frac{6}{5}$

$\dpi{80} \fn_phv cos^2\theta-sin^2\theta=\frac{4}{5}-\frac{1}{5}=\frac{3}{5}$

$\dpi{80} \fn_phv 2 sin\theta$ $\dpi{80} \fn_phv cos$ $\dpi{80} \fn_phv \theta$ $\dpi{80} \fn_phv =2\times \frac{1}{\sqrt{5}}\times \frac{2}{\sqrt{5}}=\frac{4}{5}$

Ascending order: $\dpi{80} \fn_phv \frac{3}{5},\frac{4}{5},\frac{6}{5}$

$\dpi{80} \fn_phv \rightarrow$   $\dpi{80} \fn_phv (cos^2 \theta-sin^2 \theta)(2sin\theta cos\theta),(1+sin^2 \theta)$

View Contents
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)
Self Learning
Testimonials
PARENT RESPONSE c/o Manya C/o ABHYAS Academy
8th
We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

#### Other Testimonials

Courses We Offer
(Concept based Learning and Testing for [6th - 10th], NTSE, Bank & Govt. Exams)