Question

cot theta + cosec theta = 4 then value of cos theta?

Answer 1

you can see your answer

Answer 2

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

$cot \theta +cosec \theta=4$

$\frac{cos \theta}{sin \theta} +\frac{1}{sin \theta} =4$

$cos \theta+1=4 sin \theta$

$cos \theta=cos^2 \theta/2-sin^2 \theta/2$

and, $cos^2 \theta/2+sin^2 \theta/2=1$

then,

$cos^2 \theta/2+sin^2 \theta/2+cos^2 \theta/2-sin^2 \theta/2$

$=4.2 sin \theta/2.cos \theta/2$

$2cos^2 \theta/2 =4.2 sin \theta/2 -cos \theta/2$

$cos \theta/2 =4 sin \theta/2$

$tan \theta/2=\frac{1}{4}$

$tan \theta=\frac{2 tan \thetav/2}{1-tan^2 \theta/2} =\frac{21 \times -1/4}{1- 1/16}$

$tan \theta=\frac{1/2}{15/16}$

$=\frac{8}{15}$

$AC=17$

$cosA=\frac{15}{17}$

#SPJ2