Math, asked by dummasaiaishwarya, 11 days ago

If cosα=3/5 and cosβ=5/13,where α,β are acute angles.then prove that​

Answers

Answered by surajjaiswal27236
0

Answer:

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Step-by-step explanation:

cosα=

5

3

⇒sinα=

5

4

and cosβ=

13

5

⇒sinβ=

13

12

Then

sinα+sinβ=

5

4

+

13

12

=

65

112

....(1)

cosα+cosβ=

5

3

+

13

5

=

65

64

....(2)

Adding and squaring (1) and (2), we get

sin

2

α+sin

2

β+2sinαsinβ+cos

2

α+cos

2

β+2cosαcosβ=

65

256

⇒2cos(α−β)=

65

256

−2=

65

126

⇒cos(α−β)=

65

63

A) Using cos2x=1−2sin

2

x⇒sin

2

x=

2

1−cos2x

We get

sin

2

(

2

α−β

)=

2

1−

65

63

=

65

1

B) Using cos2x=2cos

2

x−1⇒cos

2

x=

2

cos2x+1

cos

2

(

2

α−β

)=

65

64

C) tan

2

(

2

α−β

)=

cos

2

(

2

α−β

)

sin

2

(

2

α−β

)

=

65

64

65

1

=

64

1

D) sin(α+β)=sinαcos+cosαsinβ

=

5

4

×

13

5

+

5

3

×

13

12

=

65

56

Answered by saravasagadekar127
1

Step-by-step explanation:

cosα=3/5 and cosβ=5/13,where α,β are acute angles.then prove that

Using cos2x=1−2sin2x⇒sin2x=21−cos2x

We get

sin2(2α−β)=21−6563=651

B) Using cos2x=2cos2x−1⇒cos2x=2cos2x+1

cos2(2α−β)=6564

C) tan2(2α−β)=cos2(2α−β)sin2(2α−β)=6564

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