Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

Evaluate the expression:
${\text{4}}{\cot ^2}{45^0} - {\sec ^2}{60^0} + {\sin ^2}{60^0} + {\cos ^2}{90^0}$

seo-qna
Last updated date: 27th Mar 2024
Total views: 419.7k
Views today: 5.19k
MVSAT 2024
Answer
VerifiedVerified
419.7k+ views
Hint: Try to evaluate after putting values of trigonometric terms.

Given expression: ${\text{4}}{\cot ^2}{45^0} - {\sec ^2}{60^0} + {\sin ^2}{60^0} + {\cos ^2}{90^0}{\text{ }} \ldots \left( 1 \right)$
Here, we know:
$\cot {45^0} = 1,{\text{ }}\sec {60^0} = 2,{\text{ }}\sin {60^0} = \sqrt {\dfrac{3}{2}} {\text{ and }}\cos {90^0} = 0$
Therefore, putting these values in equation $\left( 1 \right)$, we get
$
  {\text{ = 4}}{\left( 1 \right)^2} - {\left( 2 \right)^2} + {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^2} + {\left( 0 \right)^2} \\
   = 4 - 4 + \left( {\dfrac{3}{4}} \right) + 0 \\
   = \dfrac{3}{4} \\
$

Note: Whenever there are angles inside trigonometric functions whose values are known to us, always try to solve by putting the values. Also, try to keep in mind the values of trigonometric functions at some specific angles like ${0^0},{30^0},{45^0},{60^0},{90^0}$as these are used frequently.
Recently Updated Pages