Evaluate the following: \( \dfrac{5cos^260° + 4sec^230° – tan^245°}{sin^2 30° + cos^2 30°}\)

Asked by Pragya Singh | 1 year ago |  76

1 Answer

Solution :-

We know that,

cos 60° = \( \dfrac{1}{2}\)

sec 30° = \( \dfrac{2}{\sqrt{3}}\)

tan 45° = 1

sin 30° = \( \dfrac{1}{2}\)

cos 30° = \( \dfrac{\sqrt{3}}{2}\)

Now, substitute the values in the given problem, we get

\( \dfrac{(5cos^260° + 4sec^230° – tan^245°)}{(sin^2 30° + cos^2 30°)} \)

= 5 \( (\dfrac{1}{2})^2\)+4 \(( \dfrac{2}{\sqrt{3}})^2-\)\(\dfrac{-1^2}{(\dfrac{1}{2^2})}\)+(\( \dfrac{\sqrt{3}}{2}\))2

 \( \dfrac{5}{4}+\dfrac{16}{3-1}\)

\( \dfrac{1}{4}+\dfrac{3}{4}\)

\( \dfrac{15+64-12}{12}\)\( \dfrac{4}{4}\)

\( \dfrac{67}{12}\)

Answered by Abhisek | 1 year ago

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