If sin -A - B- - 1- cos -A - B- - 1 and nbsp-0- nbsp- lt- A-B - nbsp-90- find A and B- 60- - nbsp-30-45- - nbsp-45-30- - nbsp-60-15- - nbsp-75-

The correct option is B 45^∘ , nbsp;45^∘ 0^∘ nbsp; lt; A+B ≤ 90^∘ (given) sin (A + B) = 1 only when A + B = 90^∘ nbsp;………… (1) cos (A – B) = 1, only wh ...

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Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

If sin (A + B...

Question

If sin (A + B) = 1, cos (A – B) = 1 and $0^{\circ} < A + B \leq 90^{\circ}$ , find A and B.

$60^{\circ}$ , $30^{\circ}$

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$45^{\circ}$ , $45^{\circ}$

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$30^{\circ}$ , $60^{\circ}$

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$15^{\circ}$ , $75^{\circ}$

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Solution

The correct option is B
$45^{\circ}$ , $45^{\circ}$

$0^{\circ} < A + B \leq 90^{\circ}$ (given)

sin (A + B) = 1 only when A + B = $90^{\circ}$ ………… (1)

cos (A – B) = 1, only when A - B = $0^{\circ}$ ………… (2)

Adding (1) and (2) we get,
2A = $90^{\circ}$
So, A = $45^{\circ}$

and as A - B = $0^{\circ}$
B = A - $0^{\circ}$ = $45^{\circ}$ - $0^{\circ}$ = $45^{\circ}$

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Similar questions

Choose the correct option and justify your choice.

(i)

(A). sin60°

(B). cos60°

(C). tan60°

(D). sin30°

(ii)

(A). tan90°

(B). 1

(C). sin45°

(D). 0

(iii) sin2A = 2sinA is true when A =

(A). 0°

(B). 30°

(C). 45°

(D). 60°

(iv)

(A). cos60°

(B). sin60°

(C). tan60°

(D). sin30°

Q. If sin (A + B) = 1 and cos (A − B) =

\frac{\sqrt{3}}{2}

, where A > B, then B = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Q. If

\sin (A - B) = \frac{1}{2} and \cos (A + B) = \frac{1}{2}, 0 ° < (A + B) \leq 90 ° and A > B

then values of A and B are
(a) (60°, 30°)
(b) (60°, 15°)
(c) (45°, 15°)
(d) (60°, 25°)

Q. If A and B are acute angles such that sin A = cos B then (A + B) = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

If $sin (A + B) = 1, cos (A - B) = 1, 0^{\circ} \leq A + B \leq 90^{\circ}$ , Find $A$ and $B$ .

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If sin (A + B) = 1, cos (A – B) = 1 and 0∘<A+B≤90∘, find A and B.

The correct option is B 45∘ , 45∘ 0∘<A+B≤90∘ (given) sin (A + B) = 1 only when A + B = 90∘ ………… (1) cos (A – B) = 1, only when A - B = 0∘ ………… (2) Adding (1) and (2) we get, 2A = 90∘ So, A = 45∘ and as A - B = 0∘ B = A - 0∘ = 45∘ - 0∘ = 45∘

If sin (A + B) = 1, cos (A – B) = 1 and $0^{\circ} < A + B \leq 90^{\circ}$ , find A and B.