Question

Evaluate
$\frac{5 cos^2 60° +4 sec^2 30° - tan^2 45°}{sin^2 30° + cos^2 30° }$
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Answer 1

Answer:

5cos²60°+4sec²30°-tan²45°/sin²30°+cos²30°.

cos60°=1/2.

sec30°=2/√3.

tan45°=1.

sin30°=1/2.

cos30°=√3/2.

5cos²60°+4sec²30°-tan²45°/sin²30°+cos²30°=5(1/2)²+4(2/√3)²-(1)²/(1/2)²+(√3/2)².

=5(1/4)+4(4/3)-1/(1/4)+(3/4).

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

=15+64-12/12/1+3/4. (Because LCM of 4 & 3 is 12).

=79-12/12/4/4.

=67/12/1.

=67/12.

I think this is your answer.