Question

If tanA=1 in a right angled ABC: right angled at C, prove that
2 sin^A cos^A=1.​

Answer 1

Given :-

In a right angled triangle ABC right angled at C and tan A = 1

Required To Prove:-

2 sin A cos A = 1

Solution :-

Given that

In a right angled triangle ABC right angled at C.

tan A = 1

=> tan A = tan 45°

=> A = 45°

Therefore, A = 45°

In taking LHS : 2 sin A cos A

=> LHS = 2 sin 45° cos 45°

=> LHS = 2 (1/√2)(1/√2)

=> LHS = 2(1/√2)²

=> LHS = 2(1/2)

=> LHS = 2/2

=> LHS = 1

=> LHS = RHS

Therefore, 2 sin A cos A = 1

Hence , Proved.

Used formulae:-

♦ sin 45° = 1/√2

♦ cos 45° = 1/√2

♦ tan 45° = 1

Answer 2

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Given :

In a right angled triangle ABC right angled at C and tan A = 1

Required To Prove:

2 sin A cos A = 1

Solution :

Given that

In a right angled triangle ABC right

angled at C.

tan A = 1

=> tan A = tan 45º

=> A = 45°

Therefore, A = 45°

In taking LHS: 2 sin A cos A

=> LHS = 2 sin 45° cos 45º

=> LHS = 2 (1/√2)(1/-√2)

=> LHS = 2(1/√/2)²

=> LHS = 2(1/2)

=> LHS = 2/2

=> LHS = 1

=> LHS = RHS

Therefore, 2 sin A cos A = 1

Hence, Proved.

Used formulae:

sin 45º = 1/√2

cos 45º = 1/√2