SEAMO 2027 - Paper F - SET 07 - Self-study Question 22

Question 22

Given $\tan\alpha=\sqrt2$, evaluate $\sin^2\alpha+2\sin\alpha\cos\alpha+3\cos^2\alpha$.

$(5+2\sqrt2)/3$
$(5+3\sqrt2)/3$
$(2+3\sqrt2)/3$
$(3+5\sqrt2)/4$
$(6+\sqrt2)/7$