The Total solution for NCERT class 6-12
Answer - 11 : -
Let us consider LHS:
By using the formula,
tan θ = sin θ / cos θ;
cot θ = cos θ / sin θ
Now,
By using the formula, a3 + b3 =(a + b) (a2 + b2– ab)
We know, sin2 x + cos2 x= 1.
1 – 1 + sin x cos x
Sin x cos x
= RHS
∴ LHS = RHS
Hence proved.
Answer - 12 : -
cosec θ = 1/sin θ,
sec θ = 1/cos θ;
Answer - 13 : -
Let us consider LHS: (1 + tan α tan β) 2 +(tan α – tan β) 2
1+ tan2 α tan2 β + 2tan α tan β + tan2 α + tan2 β – 2 tan α tan β
1 + tan2 α tan2 β + tan2 α+ tan2 β
tan2 α (tan2 β + 1) +1 (1 + tan2 β)
(1 + tan2 β) (1 + tan2 α)
We know, 1 + tan2 θ = sec2 θ
So,
sec2 α sec2 β