Verify the following identities: (a) #2sin^2(2x) + cos4x=1# (b) #tanx+co x =2sec2x# (c) #tan3x =[tanx(3-tan^2x)]/ (1-3tan^2x)#?
2 Answers
Verify:
1. 2sin^2 (2x) + cos 4x = 1
2. tan x + cot x = 2csc 2x
Explanation:
-
#2sin^2 (2x) + cos 4x = 2sin^2 (2x) + (1 - 2sin^2 (2x) = 1#
Reminder of trig identity:#cos 2a = 1 - 2sin^2 a# -
#tan x + cot x = sin x/cos x + cos x/sin x =#
=# (sin^2 x + cos^2 x)/(sin x.cos x) = 1/(sin x.cos x) =#
#= 2/(sin 2x) = 2csc (2x)#
Verify:
Explanation:
Reminder: Trig identity
Trig Identity:
Substitute into (3) the value of tan 2x from Identity (1)
Develop the numerator:
Develop the denominator: