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Evaluate the following (5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30°+cos^2 30°) - Mathematics

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Question

Evaluate the following

`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30°+cos^2 30°)`

Solution

`(5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30°+cos^2 30°)`

`(5(1/2)^2 + 4(2/sqrt3)^2 - (1)^2)/((1/2)^2 + ((sqrt3)/2)^2)`

`=(5(1/4)+(16/3)-1)/(1/4+3/4)`

`= ((15+64-12)/12)/(4/4) = 67/12`

 

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 8: Introduction to Trigonometry
Ex. 8.2 | Q: 1.5 | Page no. 187
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Evaluate the following (5cos^2 60° + 4sec^2 30° - tan^2 45°)/(sin^2 30°+cos^2 30°) Concept: Trigonometric Ratios of Some Specific Angles.
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