Question

If sin a =1/4 and cos ß= 1/4, then a + ß​

Answer 1

Step-by-step explanation:





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Class 11

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>>Trigonometric Functions

>>Trigonometric Functions of Sum and Difference of Two angles

>>sinalpha + sinbeta = 1/4 and cosalpha +

Question



sinα+sinβ=41 and cosα+cosβ=31

The value of tan(α+β) is

A

725

B

1225

C

1325

D

724

Medium

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Solution



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Correct option is D)

sinα+sinβ=3                 (i)

$$\Rightarrow 2 \sin\left (\frac{\alpha + \beta} {2}

 \right )  \cos\left (\frac{\alpha - \beta} {2}  \right ) =

3$$         (ii)

cosα+cosβ=4       (iii)

$$\Rightarrow 2 \cos\left (\frac{\alpha + \beta} {2}

 \right ) \cos\left (\frac{\alpha - \beta} {2}  \right ) =

4$$        (iv)

Dividing Eq. (ii) by Eq. (i), we have

$$\tan\left ( \frac{\alpha + \beta} {2} \right )  = \frac{3}

{4}$$

⇒sin(α+β)=1+tan2(2α+β)2tan(2α+β)=1+(43)2

Answer 2

Answer:

a + B = 90

Step-by-step explanation:

Sin A = 1/4 = Cos B = Sin (90-B)

therefore A = 90 - B

therefore A + B = 90