Question

answer pls friends my mom keeping ST​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

1) First take the L.H.S

cos 100 .cos40 + sin 100.sin40

Here we use the formula,

cos (a-b) = cos a cos b + sin a sin b

Then L.H.S becomes,

cos (100–40) = cos 60 = 1/2 = R.H.S (proved)

2)

The trigonometric identities

2cos A cos B = cos(A+B) + cos(A-B)

2sin A sin B = cos(A-B) - cos(A+B)

should be used here.

Now

cos 340° cos 40°

= (1/2)[cos(340°+40°) + cos(340°-40°)]

= (1/2)[cos 380° + cos 300°]

= (1/2)[cos(360°+20°) + cos(360°-60°)]

Now, we have to know that

cos (360°+A) = cos A

cos (360°-A) = cos(-A) = cos A [Since, cos x is an even function].

Therefore,

cos 340° cos 40° = (1/2)[ cos 20° + cos 60° ]

Now,

sin 200° sin 140°

= (1/2)[cos(200°-140°) - cos(200°+140°)]

= (1/2)[cos 60° - cos 340°]

= (1/2)[cos 60° - cos (360°-20°)]

sin 200° sin 140° = (1/2)[cos 60° - cos 20°]

Therefore,

cos 340° cos 40° + sin 200° sin 140°

= (1/2)[cos 20° + cos 60°] + (1/2)[cos 60° - cos 20°]

Taking 1/2 in common,

= (1/2)[cos 20° + cos 60° + cos 60° - cos 20°]

Cancel out cos 20°.

= (1/2)×[2cos 60°]

We know cos 60° = 1/2

= (1/2)×[2×(1/2)] = (1/2)×1

= 1/2

here is your answer

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Answer 2

Answer:

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