answer pls friends my mom keeping ST
Answers
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:
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