# Find the value of ${\text{si}}{{\text{n}}^2}18^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $.

Last updated date: 26th Mar 2023

•

Total views: 306.3k

•

Views today: 6.83k

Answer

Verified

306.3k+ views

Hint –To simplify the equation in the given question we use trigonometric identities and covert the sine function into cosine function or vice versa.

Complete step-by-step answer:

${\text{si}}{{\text{n}}^2}18^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $

⟹${\text{si}}{{\text{n}}^2}\left( {90 - 72} \right)^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $ ---- sin (90 – θ) = cosθ, since sine is a periodic function.

⟹${\text{co}}{{\text{s}}^2}72^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $

⟹0

Hence, ${\text{si}}{{\text{n}}^2}18^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $ = 0

Note: In order to solve this type of question the key is to use the right trigonometric functions and covert one of the trigonometric ratios to another to simplify the equation. Then we solve the obtained function using the trigonometric table.

Complete step-by-step answer:

${\text{si}}{{\text{n}}^2}18^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $

⟹${\text{si}}{{\text{n}}^2}\left( {90 - 72} \right)^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $ ---- sin (90 – θ) = cosθ, since sine is a periodic function.

⟹${\text{co}}{{\text{s}}^2}72^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $

⟹0

Hence, ${\text{si}}{{\text{n}}^2}18^\circ - {\text{ co}}{{\text{s}}^2}72^\circ $ = 0

Note: In order to solve this type of question the key is to use the right trigonometric functions and covert one of the trigonometric ratios to another to simplify the equation. Then we solve the obtained function using the trigonometric table.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?