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The value of cot70° + 4cot70° is A.4. B.1/2. C.√3. D.1/√3

The value of cot70° + 4cot70° is A.4. B.1/2. C.√3. D.1/√3

Grade:11

1 Answers

somi teez
105 Points
5 years ago
hi,
i think your question is cot 70+4 cos70
now proceeding,
=cos 70/sin 70 +4 cos 70
=(cos70+4sin70*cos 70)/sin 70
=(cos 70+2 sin 140)/sin 70       (using formula sin2 theta=2 sin theta *cos theta)
=(cos 70+2sin 40)/sin 70.....(using sin(180-140)=sin 40
=(cos 70+2 cos 50)/sin 70..........using sin(90-50)=cos 40
(cos 70+cos 50+cos 50)/sin 70
=(2 cos 60*cos 10+cos 50)/sin 70
=(cos 10+cos 50)/sin 70.....cos 60=1/2
=(2cos 30*cos 20)/sin 70
=(2 cos 30*sin 70)/sin 70
=2cos 30
=sqrt(3)...............answer

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