Q. 125.0( 1 Vote )

# For any Δ ABC show that -

Answer :

**Note:** In any ΔABC we define ‘a’ as the length of the side opposite to ∠A, ‘b’ as the length of the side opposite to ∠B and ‘c’ as the length of the side opposite to ∠C.

**The key** **point to solve the problem:**

The idea of cosine formula in ΔABC

• Cos A =

• Cos B =

• Cos C =

As we have to prove:

The form required to prove contains similar terms as present in cosine formula.

∴ Cosine formula is the perfect tool for solving the problem.

As we see the expression has bc term so we will apply the formula of cosA

As cos A =

⇒ 2bc cos A = b^{2} + c^{2} – a^{2}

We need (b + c )^{2} in our proof so adding 2bc both sides –

∴ 2bc + 2bc cos A = b^{2} + c^{2} +2bc – a^{2}

⇒ 2bc ( 1 + cos A) = (b + c)^{2} - a^{2}

∵ 1 + cos A = 2cos^{2} (A / 2) { using multiple angle formulae }

∴

⇒ **…..Hence proved.**

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RD Sharma - MathematicsFor any Δ ABC show that -

RD Sharma - MathematicsFor any Δ ABC show that -

RD Sharma - Mathematics