Question
Prove that:
$\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ=2$
$\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ=2$
✓
Answer
$\text{L.H.S}=\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ$
$=\sin48\sec(90^\circ-48^\circ)+\cos48^\circ\text{cosec }(90^\circ-48^\circ)$
$=\sin48^\circ\cdot\text{cosec }48^\circ+\cos48^\circ\cdot\sec48^\circ$
$=\sin48^\circ\times\frac{1}{\sin48^\circ}+\cos48^\circ\times\frac{1}{\cos48^\circ}$
$=1+1$
$=2$
$=\text{R.H.S}$
$=\sin48\sec(90^\circ-48^\circ)+\cos48^\circ\text{cosec }(90^\circ-48^\circ)$
$=\sin48^\circ\cdot\text{cosec }48^\circ+\cos48^\circ\cdot\sec48^\circ$
$=\sin48^\circ\times\frac{1}{\sin48^\circ}+\cos48^\circ\times\frac{1}{\cos48^\circ}$
$=1+1$
$=2$
$=\text{R.H.S}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The distributions $X$ and $Y$ with total number of observations $36$ and $64,$ and mean $4$ and $3$ respectively are combined. What is the mean of resulting distribution $X + Y?$
→In the given figure, $\angle$ $ACB = 90^\circ$ and $CD$ $\perp$ $AB$. prove that $\frac { B C ^ { 2 } } { A C ^ { 2 } } = \frac { B D } { A D }$.
→Find the sum of first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.
→Prove the following identities:
$\cot^2\theta-\frac{1}{\sin^2\theta}=-1$
→$\cot^2\theta-\frac{1}{\sin^2\theta}=-1$
Prove that:
$\sin(50^\circ+\theta)-\cos(40^\circ-\theta)\\+\tan1^\circ+\tan10^\circ\tan80^\circ\tan89^\circ=1$
→$\sin(50^\circ+\theta)-\cos(40^\circ-\theta)\\+\tan1^\circ+\tan10^\circ\tan80^\circ\tan89^\circ=1$
Express the following in terms of trigonometric ratios of angles lying between $0^\circ $ and $45^\circ .$
$\cos78^\circ+\sec78^\circ$
→$\cos78^\circ+\sec78^\circ$
Find:
$18^{th}$ term of the A.P. $\sqrt{2},3\sqrt{2},5\sqrt{2},\ .....$
→$18^{th}$ term of the A.P. $\sqrt{2},3\sqrt{2},5\sqrt{2},\ .....$
Find the area of $\triangle\text{ABC}$ whose vertices are:
$A(3, 8), B(-4, 2)$ and $C(5, -1)$
→$A(3, 8), B(-4, 2)$ and $C(5, -1)$
The minute hand of a clock is $12\ cm$ long. Find the area swept by in it $35$ minutes.
→Prove that $(\sin A+\operatorname{cosec} A)^2+(\cos A+\sec A)^2=7+\tan ^2 A+\cot ^2 A$.
→