標題:
A maths Trigonometry
發問:
1. In triangle ABC, if sin C= (sin A+sin B)/(cos A+cos B), prove that triangle ABC is a right triangle. 2. Find the maximum value and minimum value of 3/(4(cos x)^2+5)-1 更新: The answer of question 2 is -2/5 and 2/5, How can I get the answer??
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最佳解答:
1 In triangle ABC, if sin C= (sin A+sin B)/(cos A+cos B), prove that triangle ABC is a right triangle. SOLUTION sin A + sin B sin C = -------------------- --- cos A + cos B sin C=(sin A + sin B)/(cos A + cos B) sin C=(sin (A+B)/2 cos(A- B)/2)/(cos (A+B)/2 cos (A-B)/2) sin C=(sin (90-C/2) cos(A- B)/2)/(cos (90-C/2) cos (A-B)/2) sin C=cos (C/2) /sin (C/2) 2(sinC/2)(cosC/2)=co s (C/2) /sin (C/2) sin^2(C/2)=1/2 So C/2=45 C=90 ?ABC is a right-angled triangle and C is the right-angled Note: (A+B)/2=(180-C)/2=90-C/2 2 Find the maximum value and minimum value of 3/(4(cos x)^2+5)-1 SOLUTION Because -1
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