Question
Without using trigonometric identity, show that :
$
\sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ}=2
$
$
\sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ}=2
$
✓
Answer
$
\begin{aligned}
& \sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ}=2 \\
& \text { consider } \sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ} \\
& \Rightarrow \sin 42^{\circ} \sec \left(90^{\circ}-42^{\circ}\right)+\cos 42^{\circ} \operatorname{cosec}\left(90^{\circ}-42^{\circ}\right) \\
& \Rightarrow \sin 42^{\circ} \cdot \operatorname{cosec} 42^{\circ}+\cos 42^{\circ} \sec 42^{\circ} \\
& \Rightarrow \sin 42^{\circ} \cdot \frac{1}{\sin 42^{\circ}}+\cos 42^{\circ} \frac{1}{\cos 42^{\circ}} \\
& \Rightarrow 1+1=2
\end{aligned}
$
\begin{aligned}
& \sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ}=2 \\
& \text { consider } \sin 42^{\circ} \sec 48^{\circ}+\cos 42^{\circ} \cos e c 48^{\circ} \\
& \Rightarrow \sin 42^{\circ} \sec \left(90^{\circ}-42^{\circ}\right)+\cos 42^{\circ} \operatorname{cosec}\left(90^{\circ}-42^{\circ}\right) \\
& \Rightarrow \sin 42^{\circ} \cdot \operatorname{cosec} 42^{\circ}+\cos 42^{\circ} \sec 42^{\circ} \\
& \Rightarrow \sin 42^{\circ} \cdot \frac{1}{\sin 42^{\circ}}+\cos 42^{\circ} \frac{1}{\cos 42^{\circ}} \\
& \Rightarrow 1+1=2
\end{aligned}
$
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
Determine whether the given quadratic equations have equal roots and if so, find the roots:
$3x^2 - 6x + 5 = 0$
→$3x^2 - 6x + 5 = 0$
Find x and y if 3[4 x] + 2[y -3] = [10 0]
Find the mode of following data, using a histogram:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 5 | 12 | 20 | 9 | 4 |
In the following figure, the line of symmetry has been drawn with a dotted line. Identify the corresponding sides and the corresponding angles about the line of symmetry.
State the co-ordinates of the following points under reflection in y-axis:
(i) (6, -3)
(ii) (-1, 0)
(iii) (-8, -2)
Find the mean proportional between $6+3 \sqrt{3}$ and $8-4 \sqrt{3}$
→Represent the following inequalities on real number lines
$2(2 x-3) \leq 6$
→$2(2 x-3) \leq 6$
Find the ratio of the following in the simplest fcrm:
$a^4 + b^4$ and $a^3 - b^3$
→$a^4 + b^4$ and $a^3 - b^3$
A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.
Find the value of k for which equation $4 x^2+8 x-k=0$ has real roots.
→