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plz tell me how to solve the question? cos α + cos β=3/2 and sin α + sin β =1/2 and θ the arithmetic mean of α and β,then sin 2 θ + cos 2 θ is equal to (a)3/5 (b)4/5 (c)7/5 (d)8/5

plz tell me how to solve the question?
cosα + cosβ=3/2 and sinα + sinβ =1/2 and θ the arithmetic mean of α and β,then sin 2θ + cos 2θ is equal to
(a)3/5    (b)4/5   (c)7/5   (d)8/5
 

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Grade:12th Pass

1 Answers

dip
24 Points
7 years ago
2cos(\alpha +\beta )/2cos(\alpha -\beta )/2=3/2 ......(1)........... sin\alpha +sin\beta =1/2 .......... 2sin(\alpha +\beta )/2cos(\alpha -\beta )/2=1/2..........(2)................ ...... (1)/(2) we..... get, tan(\alpha +\beta )/2=1/3........................ and (\alpha +\beta )/2=\theta ........so... tan\theta =1/3 ........ again .....cos2\theta +sin2\theta =(1-tan^{2}\theta )/(1+ tan^{2}\theta ) +2tan\theta /(1+ tan^{2}\theta )..... By .......putting ..........value .......of ..... tan\theta..... we..... get .....ans:.===7/5...........(3)In order to answer this question we use use the formulas ofsinA +sinB =2sin(A+B)/2cos(A-B)/2and cosA+cosB=2cos(A+B)/2cos(A-B)/2In this way the answer comes out to be 7/5

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