已知2sin(3pai+a)=cos(pai+a),求2(sina)^2+3sinacosa-(cosa)^2的值.

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已知2sin(3pai+a)=cos(pai+a),求2(sina)^2+3sinacosa-(cosa)^2的值.

已知2sin(3pai+a)=cos(pai+a),求2(sina)^2+3sinacosa-(cosa)^2的值.
已知2sin(3pai+a)=cos(pai+a),求2(sina)^2+3sinacosa-(cosa)^2的值.

已知2sin(3pai+a)=cos(pai+a),求2(sina)^2+3sinacosa-(cosa)^2的值.
∵2sin(3π+a)=cos(π+a),
∴2sina=cosa,则tana=1/2.
故2(sina)²+3sinacosa-(cosa)²
=(sin²a/cos²a+3sina/cosa-1)/cos²a
=(tan²a+3tana-1)sec²a
=(tan²a+3tana-1)(1+tan²a)
=[(1/2)²+3(1/2)-1][1+(1/2)²]
=15/16