The Total solution for NCERT class 6-12
Answer - 1 : -
Answer - 2 : -
Answer - 3 : -
Answer - 4 : -
Answer - 5 : -
Answer - 6 : -
Answer - 7 : -
Answer - 8 : -
It is given that
sec2 2x= 1 – tan 2x
We can write it as
1 + tan2 2x= 1 – tan 2x
tan2 2x+ tan 2x = 0
Taking common terms
tan 2x (tan 2x + 1) =0
Here
tan 2x = 0 or tan 2x +1 = 0
If tan 2x = 0
tan 2x = tan 0
We get
2x = nπ + 0, where n ∈ Z
x = nπ/2, where n ∈ Z
tan 2x + 1 = 0
tan 2x = – 1
So we get
2x = nπ + 3π/4, wheren ∈ Z
x = nπ/2 + 3π/8, wheren ∈ Z
Hence, the generalsolution is nπ/2 or nπ/2 + 3π/8, n ∈ Z.
Answer - 9 : -
By further calculation
2 sin 3x cos (-2x) +sin 3x = 0
It can be written as
2 sin 3x cos 2x + sin3x = 0
By taking out thecommon terms
sin 3x (2 cos 2x + 1)= 0
sin 3x = 0 or 2 cos 2x+ 1 = 0
If sin 3x = 0
3x = nπ, where n ∈ Z
x = nπ/3, where n ∈ Z
If 2 cos 2x + 1 = 0
cos 2x = – 1/2
By furthersimplification
= – cos π/3
= cos (π – π/3)
cos 2x = cos 2π/3