Download App

Trigonometric Ratios of Complementary Angles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Ratios of Complementary Angles1 Mark
Question
Without using trigomentric tables, prove that:
$\sec70^\circ\sin20^\circ+\cos20^\circ\text{cosec}70^\circ=2$
✓

Answer

$\text{L.H.S}=\sec70^\circ\sin20^\circ+\cos20^\circ\text{cosec}70^\circ$
$=\sec\big(90^\circ-20^\circ\big)\sin20^\circ+\cos20^\circ\text{cosec}\big(90^\circ-20^\circ\big)$
$=\text{cosec}20^\circ.\frac{1}{\text{cosec}20^\circ}+\frac{1}{\sec20^\circ}.\sec20^\circ$
$=1+1$
$=2$
$=\text{R.H.S.}$

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 "1 Marks Question" from Trigonometric Ratios of Complementary Angles→Trigonometric Ratios of Complementary Angles — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Prove that:
cot θ + tan θ = cosec θ sec θ
→
Very-Short-Answer Questions.
A coin is tossed once. What is the probability of getting a tail?
→
Without using trignometric tables, prove that:
$\cos^257^\circ+\sin^233^\circ=0$
→
Write the roots of following quadratic equation.
(p – 5 ) (p + 3 ) = 0
→
If 50 shares of FV ₹ 100 each are purchased for MV ₹ 120. Find the sum invested.
→
$x^2 + 4x – 5 = 0, x = 1, -1$
→
If the total value of the mutual fund scheme is ₹ 200 crores and 8 crore units are issued then find the NAV of one unit.
→
If one root of the quadratic equation $3x^2 - 10x + k = 0$ is reciprocal of the other, find the value of $k$.
→
Without using trignometric tables, prove that:
$\text{cosec}80^\circ-\sec10^\circ=0$
→
The height of an equilateral triangle is $3\sqrt3\text{cm}.$ Its area is:
  1. $6\sqrt3\text{cm}^2$
  2. $27\text{cm}^2$
  3. $9\sqrt3\text{cm}^2$
  4. $27\sqrt3\text{cm}^2.$
→