Download App

Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals] — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSTrigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]2 Marks
Question
If $\sin A +  \operatorname{cosec}\ A = 2;$Find the value of $\sin^2 A + \ \operatorname{cosec}^2 A.$
✓

Answer

$\sin A+\ \operatorname{cosec} A = 2$
Squaring both sides
$(\sin A+\operatorname{cosec}\ A)^2 = 2^2$
$\sin^2 A +\operatorname{cosec}^2 A+2 \sin\ A . \operatorname{cosec}A = 4$
$\sin^2 A + \operatorname{\operatorname{cosec}}^2 A+2 \sin A$. $\frac{1}{\tan A }$ = 4
$\sin^2 A +\operatorname{cosec}^2 A =2$

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 Mark Question Answer]" from Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]→Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals] — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

Evaluate the following$: (0.008)^{\frac{2}{3}}$
→
Simplify by using formula $:\left(a+\frac{2}{a}-1\right)\left(a-\frac{2}{a}-1\right)$
→
Factorise the following by the difference of two squares$:(x - 2y)^2 -z^2$
→
The mean of $15$ observations is $32.$ Find the resulting mean $,$ if the observation is $: $ Divided by $0.5$
→
A rectangular field is 40 m long and 30 m broad. Find the length of its diagonal.
→
Without using trigonometric tables, evaluate.
$\sin 37^{\circ}-\cos 53^{\circ}$
→
Can you construct a $\triangle ABC$ in which $AB =5 cm, BC =4 cm$ and $AC =9 cm$ ? Give reason.
→
A test out of $25$ marks was given to $16$ students and marks scored are recorded below:$25, 8, 14, 20, 16, 22, 10, 15, 8, 7, 24, 18, 19, 6, 11, 14$ Find the mean marks
→
Draw the graph of:
x + 4 = 0
→
Find the value of $x$, when:
$\log _x 64=\frac{3}{2}$
→