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Exercises · Q8

Q.Evaluate: 2sin⁡230°+3cos⁡260°−tan⁡245°2\sin^230° + 3\cos^260° - \tan^245°.

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✓ Free question

Step 1 — read the standard values. sin⁡30°=12, cos⁡60°=12, tan⁡45°=1\sin30°=\frac12,\ \cos60°=\frac12,\ \tan45°=1.

Step 2 — square where needed and apply the coefficients.

2sin⁡230°=2(12)2=2⋅14=122\sin^230° = 2\left(\frac12\right)^2 = 2\cdot\frac14=\frac12

3cos⁡260°=3(12)2=3⋅14=343\cos^260° = 3\left(\frac12\right)^2 = 3\cdot\frac14=\frac34

tan⁡245°=12=1\tan^245° = 1^2 = 1

Step 3 — combine.

12+34−1=24+34−44=14\frac12+\frac34-1 = \frac{2}{4}+\frac{3}{4}-\frac{4}{4} = \frac14

✓Final answer

14\dfrac14

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