Question

If Sin (P+Q) = 1 and Sin (P - Q) = root3/2, find P and Q.​

Answer 1

Step-by-step explanation:

bvvvan if sin Q) = 1 and Sin (P - Q) = root3/2, find P a

Answer 2

Given:

• sin(P + Q) = 1
• sin(P - Q) = √3/2

To find:

☞ Value of P and Q = ?

Solution:

$\sf{sin(P+Q) = 1}\\\\\\\Rightarrow \sf{P+Q = sin^{-1}(1) }\\\\\\\Rightarrow \bf{P+Q = 90^{\circ} \quad \dashrightarrow [Equation \: 1]}$

$\\\rm{Similarly,}\\\\\sf{sin (P-Q) = \dfrac{\sqrt{3} }{2}}\\\\\\\Rightarrow \sf{(P-Q) = sin^{-1}\bigg(\dfrac{\sqrt{3} }{2}\bigg) }\\\\\\\Rightarrow \bf{P-Q = 60^{\circ} \quad \dashrightarrow [Equation \: 2]}$

Adding Equations 1 and 2,

                          P + Q = 90°

                 {+}       P - Q = 60°

                            P + P = 90° + 60°

➞ 2P = 150°

➝ P = 150 ÷ 2

∴ P = 75°

Now let's substitute value of P in Equation 1 to find the value of Q.

P + Q = 90°

➩ 75° + Q = 90°

➩ Q = 90° - 75°

∴ Q = 15°