Question

Please solve (d) in the question in image and get 100 points, hurry!!! ​

Answer 1

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• Match the following.

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Given that,

$\sin \alpha = \sin \beta$

And,

$\cos \alpha = \cos \beta$

From the trigonometry ratio table, we can say that,

$\alpha = \beta = 45 \degree$

So, now we will evaluate each expression of column 1.

Number A.

$\sin( \frac{ \alpha - \beta }{2} )$

$= \sin0 \degree = 0$

So,

(A) matches with (P)

Number B.

$\sin2 \alpha + \sin2 \beta$

$= \sin90 \degree + \sin90 \degree$

$= 1 + 1$

$= 2$

$= 2 \sin(90 \degree)$

$= 2 \sin( \alpha + \beta )$

Therefore,

(B) matches With (S)

Number C.

$\cos( \alpha + \beta )$

$= \cos(90 \degree)$

$= 0$

$= 2 \times \cos(90 \degree)$

$= 2 \cos(45 \degree + 45 \degree)$

$= 2 \cos( \alpha + \beta )$

So,

(C) matches with (Q).

Number D.

$\tan( \frac{ \alpha + \beta }{2} )$

$= \tan(45 \degree)$

$= 1$

So,

(D) Matches with R.

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• (A) matches with (P)
• (B) matches with (S)
• (C) matches with (Q)
• (D) matches with (R)

Answer 2

Answer:

Given that,

\sin \alpha = \sin \betasinα=sinβ

And,

\cos \alpha = \cos \betacosα=cosβ

From the trigonometry ratio table, we can say that,

\alpha = \beta = 45 \degreeα=β=45°

So, now we will evaluate each expression of column 1.

Number A.

\sin( \frac{ \alpha - \beta }{2} )sin(

2

α−β

)

= \sin0 \degree = 0=sin0°=0

So,

(A) matches with (P)

Number B.

\sin2 \alpha + \sin2 \betasin2α+sin2β

= \sin90 \degree + \sin90 \degree=sin90°+sin90°

= 1 + 1=1+1

= 2=2

= 2 \sin(90 \degree)=2sin(90°)

= 2 \sin( \alpha + \beta )=2sin(α+β)

Therefore,

(B) matches With (S)

Number C.

\cos( \alpha + \beta )cos(α+β)

= \cos(90 \degree)=cos(90°)

= 0=0

= 2 \times \cos(90 \degree)=2×cos(90°)

= 2 \cos(45 \degree + 45 \degree)=2cos(45°+45°)

= 2 \cos( \alpha + \beta )=2cos(α+β)

So,

(C) matches with (Q).

Number D.

\tan( \frac{ \alpha + \beta }{2} )tan(

2

α+β

)

= \tan(45 \degree)=tan(45°)

= 1=1

So,

(D) Matches with R.

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Answer:−

(A) matches with (P)

(B) matches with (S)

(C) matches with (Q)

(D) matches with (R)