HSC Arts 12th Board ExamMaharashtra State Board
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# In any triangle ABC with usual notations prove c = a cos B + b cos A - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptTrigonometric Functions General Solution of Trigonometric Equation of the Type

#### Question

In any triangle ABC with usual notations prove c = a cos B + b cos A

#### Solution

By cosine rule, we have b2 = c2 + a2 - 2ca cos B

therefore cosB=(c^2+a^2-b^2)/2ac

Similarly cos A=(b^2+c^2-a^2)/(2bc)

R.H.S. = a cos B + b cos A

=a.(c^2+a^2-b^2)/(2ac)+b.(b^2+c^2-a^2)/(2bc)

=(c^2+a^2-b^2)/(2c)+(b^2+c^2-a^2)/(2c)

=(c^2+a^2-b^2+b^2+c^2-a^2)/(2c)

=(2c^2)/(2c)

=c

=L.H.s

∴ c = a cos B + b cso A

Is there an error in this question or solution?

#### APPEARS IN

2015-2016 (July) (with solutions)
Question 3.1.3 | 3.00 marks
Solution In any triangle ABC with usual notations prove c = a cos B + b cos A Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type.
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