Question

Prove that
tan 20°+ tan 70°
2 cosec 40​

Answer 1

tan 20°+ tan 70° = 2cosec 40​

• In the discipline of mathematics known as trigonometry that deals with particular functions of angles, the tangent is a function. It discusses how triangle side lengths and angles relate to one another. Using trigonometric formulas and functions, it is mostly used to determine the unknown side lengths and angles of a right-angled triangle. Six different functions are frequently employed in trigonometry.
• Along with the other 5 trigonometric functions, tan is a widely used trigonometric function. The law of tangent is another name for tan. The ratio of a triangle's opposite side to its adjacent side is known as the tangent formula for a right-angled triangle. The angle's sine to cosine ratio can also be used to express the angle.

Here, according to the given information, we are given to prove that,

tan 20°+ tan 70° = 2cosec 40​.

Now, let us first consider the left hand side.

LHS

= tan 20°+ tan 70°

= tan 20°+ tan (90-20)°

= tan 20°+ $\frac{1}{tan20}$

= $\frac{tan^{2} 20+1}{tan20}$

= $\frac{sec^{2}20 }{tan20}$

= $\frac{2}{sin40}$

= 2cosec40°

= RHS.

Hence, proved.

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