Question

if cos (A+B)=1\2 and sin (A-B)=1\2,0° <A+B≤​

Answer 1

Correct Question :-

• If cos ( A + B ) = ½ and sin ( A - B ) = ½ and the condition 0° < A + B ≤ 90°.

Given :-

• Cos ( A + B ) = ½

• Sin ( A - B ) = ½

To Find :-

• The Angles A and B

Solution :-

We are given to find out the Angles A and B in the respective identities of cos and sin.

Let consider in Each Cases.

If Cos ( A + B ) = ½

A + B = ½

We Know that Cos 60° = ½

Hence cos ( A + B ) = 60 = ½_____(1)

Considering the Next One,

Sin ( A - B ) = ½

( A - B ) = ½

We Know that Sin 30 = ½

Hence Sin(A - B ) = Sin 30 = ½ ________(2)

From Equations 1 and 2 Interchanging the values we get.

A + B = 60

A - B = 30 -

__________

2B = 30 [ We inter changed the Signs ]

Hence B = 15°

Since B = 15°

cos ( A + B ) = 60

A = 60 - 15

A = 45°

$\sf{ \rightarrow{ \pink{Hence \: A = 45 \: and \:B = 15}{} }{} }{}$

More To Know :-

• Values of Sin and Cos are interchanged hence the values of them are reciprocal to each other.

• Sin∅ = ¹/Cos∅

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