Download App

Trigonometric Ratios of Complementary Angles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTrigonometric Ratios of Complementary Angles2 Marks
Question
Prove that:
$\frac{\sin\theta}{\cos(90^\circ-\theta)}+\frac{\cos\theta}{\sin(90^\circ-\theta)}=2$
✓

Answer

$\text{L.H.S.}=\frac{\sin\theta}{\cos(90^\circ-\theta)}+\frac{\cos\theta}{\sin(90^\circ-\theta)}$
$=\frac{\sin\theta}{\sin\theta}+\frac{\cos\theta}{\cos\theta}$
$=1+1$
$=2$
$=\text{R.H.S.}$
Hence Proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Trigonometric Ratios of Complementary Angles→Trigonometric Ratios of Complementary Angles — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Very-short and Short-Answer Questions.
Write the value of $\big(1-\cos^2\theta\big)\text{cosec}^2\theta.$
→
Solve the following quadratic equations by factorization:
$(2x + 3)(3x - 7) = 0$
→
The points $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3, y_3\right)$ are the vertices of $∆ABC.$
The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D.$
→
Find the centroid of the triangle whose vertices are:
$(-2, 3) (2, -1) (4, 0).$
→
The area of a circle is $98.56\ cm^2$ find its circumference. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→
Triangle $ABC$ and $DEF$ are similar.
If $AB = 1.2\ cm$ and $DE = 1.4\ cm,$ find the retio of the areas of $\triangle\text{ABC}$ and $\triangle\text{DEF}.$
→
Write the formula for the area of the triangle having its vertices at $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$.
→
Very-Short-Answer Question:
Write the zeros of the polynomial $x^2- x - 6$
→

Prove the following identites:

$\big(1-\cos^2\theta\big)\text{cosec}^2\theta=1$

→
A ladder $15m$ long just reaches the top of a vertical wall. If the ladders makes an angle of $60^\circ$ with the wall, then find the height of the wall.
→