Question

If Sin (∝ + β) = 1 and cos (∝ − β) = 1 where ∝ + β <90, then the value of ∝ and β are respectively equal to
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Answer 1

Given :- Sin (∝ + β) = 1 and cos (∝ − β) = 1 where ∝ + β ≤ 90, then the value of ∝ and β are respectively equal to ?

Solution :-

Let ∝ is denoted as A and β is denoted as B .

so,

→ sin(A + B) = 1

using sin 90° = 1 in RHS we get,

→ sin(A + B) = sin 90°

→ A + B = 90° --------- Eqn.(1)

and,

→ cos(A - B) = 1

using cos 0° = 1 in RHS we get,

→ cos(A - B) = cos 0°

→ A - B = 0°

→ A = B --------- Eqn.(2)

putting value of A in Eqn.(1)

→ B + B = 90°

→ 2B = 90°

→ B = 45° .

therefore, values of A and B are 45° .

Hence, the value of ∝ and β are respectively equal to 45° each .

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Answer 2

Given : Sin (∝ + β) = 1 and cos (∝ − β) = 1  ∝ + β ≤ 90

To Find : value of ∝ and β

Solution:

Sin (∝ + β) = 1  

=> ∝ + β = 90°

cos (∝ − β) = 1

=> ∝ − β = 0°

Adding both

2∝ = 90°

=> ∝ = 45°

=> β = 45°

Hence value of ∝ and β are   45° each

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