Question -
Answer -
(i)
1 = RHS
∴ LHS = RHS
Hence proved.
(ii)
1 + 1
2 = RHS
∴ LHS = RHS
Hence proved.
(iii)
1 = RHS
∴ LHS = RHS
Hence proved.
(iv)
{1 + cot x – (-cosec x)} {1 + cot x + (-cosec x)}
{1 + cot x + cosec x} {1 + cot x – cosec x}
{(1 + cot x) + (cosec x)} {(1 + cot x) – (cosec x)}
By using the formula, (a + b) (a – b) = a2 –b2
(1 + cot x)2 – (cosec x)2
1 + cot2 x + 2 cot x – cosec2 x
We know that 1 + cot2 x = cosec2 x
cosec2 x + 2 cot x – cosec2 x
2 cot x = RHS
∴ LHS = RHS
Hence proved.
(v)
1 = RHS
∴ LHS = RHS
Hence proved.