Question
If $\tan\theta=\frac{24}{7},$ find that $\sin\theta+\cos\theta.$
✓
Answer
$\tan\theta=\frac{24}{7}$ find $\sin\theta+\cos\theta$
Let x - 1 be the hypotenuse By applying Pythagoras theorem we get
$\text{AC}^2=\text{AB}^2+\text{BC}^2$ $\text{x}^2=(24)^2+(7)^2$ $\text{x}^2=576+49=62.5$ $\text{x}=25$ $\sin\theta=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$ $\cos\theta=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}$ $\sin\theta+\cos\theta=\frac{24}{25}+\frac{7}{25}$ $=\frac{31}{25}$
Let x - 1 be the hypotenuse By applying Pythagoras theorem we get
$\text{AC}^2=\text{AB}^2+\text{BC}^2$ $\text{x}^2=(24)^2+(7)^2$ $\text{x}^2=576+49=62.5$ $\text{x}=25$ $\sin\theta=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$ $\cos\theta=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}$ $\sin\theta+\cos\theta=\frac{24}{25}+\frac{7}{25}$ $=\frac{31}{25}$
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
Find the mean of each of the following frequency distributions:
→|
Class interval
|
$10-30$
|
$30-50$
|
$50-70$
|
$70-90$
|
$90-110$
|
$110-130$
|
|
Frequency
|
$5$
|
$8$
|
$12$
|
$20$
|
$3$
|
$2$
|
In Figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Prove the identity: $\frac{(1+\cot A+\tan A)(\sin A-\cos A)}{\sec ^3 A-\operatorname{cosec}^3 A}=\sin ^2 A \cos ^2 A$
→Prove the following identities:
$\frac{\cos\theta}{(1-\tan\theta)}+\frac{\sin^2\theta}{(\cos\theta-\sin\theta)}=(\cos\theta+\sin\theta)$
→$\frac{\cos\theta}{(1-\tan\theta)}+\frac{\sin^2\theta}{(\cos\theta-\sin\theta)}=(\cos\theta+\sin\theta)$
Very-Short and Short-Answer Qustions:
If $\tan\theta=\frac{1}{\sqrt{5}},$ write the value of $\frac{\big(\text{cosec}^2\theta-\sec^2\theta\big)}{\big(\text{cosec}^2\theta+\sec^2\theta\big)}.$
→If $\tan\theta=\frac{1}{\sqrt{5}},$ write the value of $\frac{\big(\text{cosec}^2\theta-\sec^2\theta\big)}{\big(\text{cosec}^2\theta+\sec^2\theta\big)}.$
For what value of k, is $-3$ a zero of the polynomial $x^2 + 11x + k?$
→AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in the figure. Prove that $\angle\text{BAT}=\angle\text{ACB}.$
→Solve for x and y:
$\text{2x}-\frac{\text{3y}}4{}=3,$
$5\text{x}=2\text{y}+7$
→$\text{2x}-\frac{\text{3y}}4{}=3,$
$5\text{x}=2\text{y}+7$
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = ax^2 + bx + c$, then evaluate:$\frac{1}{\text{a}\alpha+\text{b}}+\frac{1}{\text{a}\beta+\text{b}} $
→For what value of k does the system of equations:
x + 2y = 5, 3x + ky + 15 = 0
have;
x + 2y = 5, 3x + ky + 15 = 0
have;
- A unique solution,
- No solution?