Mathematics

In $$\Delta ABC, \angle C=90^{\circ}$$ then the value of $$\sin^{2}A+\sin^{2}B$$ is :


ANSWER

$$1$$


SOLUTION
Given $$∠C={90}^o$$
From Triangle, 
$$\sin A =\cfrac {BC}{AB};$$  $$\sin B=\cfrac {AC}{AB}$$
$$\Rightarrow {\sin}^2A+{\sin}^2B$$
$$\cfrac { { BC }^{ 2 } }{ { AB }^{ 2 } } +\cfrac { { AC }^{ 2 } }{ { AB }^{ 2 } } =\cfrac { { BC }^{ 2 }+{ AC }^{ 2 } }{ { AB }^{ 2 } } $$
From $$\triangle ABC$$, by using Pythagoras Theorem,
$${AB}^2={BC}^2+{AC}^2$$
$${\sin}^2A+{\sin}^2B=\cfrac { { BC }^{ 2 }+{ AC }^{ 2 } }{ { AB }^{ 2 } }=\cfrac { { AB }^{ 2 } }{ { AB }^{ 2 } }=1 $$  
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Single Correct Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Can two acute angles form a linear pair?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Single Correct Medium
The lines which lie on the same plane and do not intersect at any point are called_______
  • A. perpendicular
  • B. intersecting
  • C. none of these
  • D. parallel

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Single Correct Medium

In given figure the value of $$x$$ is :
  • A. $$120^{\circ}$$
  • B. $$110^{\circ}$$
  • C. $$80^{\circ}$$
  • D. $$100^{\circ}$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Single Correct Medium
A transversal intersects two or more than two lines at _________ points.
  • A. Same
  • B. Two
  • C. None of these
  • D. Different

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Subjective Medium
If two angles have a common vertex and their arms form opposite rays Fig., Then, how many angles are formed?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer