Question
Prove : $\frac{\cos \theta}{1+\sin \theta}=\sec \theta-\tan \theta$
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A target shown in the figure consists of three concentric circles of radii 3, 7 and 9cm respectively. A dart is thrown and lands on the target. What is the probability that the dart will land on the shaded region?
Find the value of k for which each of the following system of equations have infinitely many solutions:
→$4x + 5y = 3$
$kx + 15y = 9$
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
$5x^2 - 4 - 8x$
→$5x^2 - 4 - 8x$
Form the simultaneous linear equation using the determinants.
$D=\left|\begin{array}{cc}4 & -3 \\ 2 & 5\end{array}\right| \quad D x=\left|\begin{array}{cc}5 & -3 \\ 9 & 5\end{array}\right| \quad D y=\left|\begin{array}{ll}4 & 5 \\ 2 & 9\end{array}\right|$
→$D=\left|\begin{array}{cc}4 & -3 \\ 2 & 5\end{array}\right| \quad D x=\left|\begin{array}{cc}5 & -3 \\ 9 & 5\end{array}\right| \quad D y=\left|\begin{array}{ll}4 & 5 \\ 2 & 9\end{array}\right|$
Solve the following simultaneous equation graphically.
3x – y – 2 = 0; 2x + y = 8
3x – y – 2 = 0; 2x + y = 8
E is a point on hypotenuse DF of $\Delta$DFH, such that seg HE $\perp$ seg DF, seg EG $\perp$ seg FH and seg EK $\perp$ seg DH. Prove that, (i) $EG ^2= FG \times EK$
(ii) $E K^2= DK \times EG$
→(ii) $E K^2= DK \times EG$
In figure 1.74, PM = 10 cm A(Δ PQS) = 100 sq.cm A (ΔQRS) = 110 sq.cm then find NR.
In a $\triangle\text{ABC,D}\ \text{and E}$ are points on the sides AB and AC respectively such that DE || BC.If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3, find the value of x.
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Find n if the given value of $x$ is the $n^{th}$ term of the given A.P.
$1,\frac{21}{11},\frac{31}{11},\frac{41}{11}, .....;\text{ x}=\frac{171}{11}.$
→$1,\frac{21}{11},\frac{31}{11},\frac{41}{11}, .....;\text{ x}=\frac{171}{11}.$