Advertisement Remove all ads

# Prove the following: 2cos2A+12cos2A-1 = tan(60° + A) tan(60° − A) - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Prove the following:

(2cos2"A" + 1)/(2cos2"A" - 1) = tan(60° + A) tan(60° − A)

Advertisement Remove all ads

#### Solution

R.H.S. = tan(60° + A) tan(60° − A)

= (sin(60^circ + "A")sin(60^circ - "A"))/(cos(60^circ + "A")cos(60^circ - "A")

= (2sin(60^circ + "A")sin(60^circ - "A"))/(2cos(60^circ + "A")cos(60^circ - "A")

= (cos[60^circ + "A" - (60^circ - "A")] - cos(60^circ + "A" + 60^circ - "A"))/(cos(60^circ + "A" + 60^circ - "A") + cos[60^circ + "A" - (60^circ - "A")]

= (cos2"A" - cos120^circ)/(cos120^circ - cos2"A")

= (cos2"A" - cos(180^circ - 60^circ))/(cos(180^circ - 60^circ) + cos2"A")

= (cos2"A" - (- cos 60^circ))/(- cos60^circ + cos2"A")

= (cos2"A" + 1/2)/(-1/2 + cos2"A")

= (2cos2"A" + 1)/(2cos2"A" - 1)

= L.H.S.

Concept: Trigonometric Functions of Sum and Difference of Angles
Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Trigonometry - 2
Miscellaneous Exercise 3 | Q II. (13) | Page 57
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?