Question
Differentiate the following function with respect to $(\text{x})$:
$\cos(\text{x}+\text{h})$
$\cos(\text{x}+\text{h})$
$\frac{\text{d}}{\text{dx}}\Big\{\cos(\text{x}+\text{h})\Big\}$
$=\frac{\text{d}}{\text{dx}}(\cos\text{x}.\cos\text{a}-\sin\text{x}.\sin\text{a})\ [\because\cos(\text{x}+\text{a})=\cos\text{x}\cos\text{a}-\sin\text{x}\sin\text{a}]$
$=\cos\text{a}\frac{\text{d}}{\text{dx}}(\cos\text{x})-\sin\text{a}\frac{\text{d}}{\text{dx}}(\sin\text{x})$
$=\cos\text{a}(-\sin\text{x})-\sin\text{a}(\cos\text{x})$
$=\cos\text{x}(\sin\text{a})+\sin\text{x}(\cos\text{a})$
$=-(\sin\text{x}\cos\text{a}+\cos\text{x}\sin\text{a})$
$=-\sin(\text{x}+\text{a})$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
If (m+1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m +n + 1)th term.