If SinA-B-1- CosA-B-1-0- A-B - 90- Find A and B-A- 45- 45-B- 60- 30-C- 30- 60-D- 15- 75-

The correct option is A If A+B lies in this range 0^∘ lt; A+B ≤ 90^∘ Sin (A + B) = 1 only when A + B = 90^∘ ............ (1) Cos (A B) = 1, only when A ...

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Standard XI

Mathematics

Solving Simultaneous Trigonometric Equations

If SinA+B=1, ...

Question

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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Solution

If $A + B$ lies in this range $0^{\circ} < A + B \leq 90^{\circ}$

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

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

Lets add eq (1) and eq (2),
$A + B + A - B = 90^{\circ} + 0^{\circ}$
$\Rightarrow 2 A = 90^{\circ}$
$\Rightarrow A = 45^{\circ}$
From(1)
$45^{\circ} + B = 90^{\circ}$
$\Rightarrow B = 45^{\circ}$
Hence, option A is correct.

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Similar questions

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°)

$If s i n A = \frac{1}{2} and c o s B = \frac{1}{\sqrt{2}}$ ,
then find the value of (A+B).

Given that $s i n A = \frac{1}{2}$ and $c o s B = \frac{1}{\sqrt{2}}$ , then find the value of $(A + B)$ .

Q. If

s i n (B + C) = \frac{\sqrt{3}}{2}

and

s i n A = \frac{1}{2}

, find

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and

A

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If sin(A+B)=1,cos(A−B)=1, 0∘≤A+B≤90∘, Find A and B.

If A+B lies in this range 0∘<A+B≤90∘ sin(A+B)=1 only when A+B=90∘ ............ (1) cos(A−B)=1, only when A−B=0∘ ............ (2) Lets add eq (1) and eq (2),A+B+A−B=90∘+0∘⇒2A=90∘⇒A=45∘From(1)45∘+B=90∘⇒B=45∘Hence, option A is correct.

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