# Beware of blind algebra!!

Here is an interesting case of a problem in trigonometry...... I had encountered this in my CET entrance exam .....

The problem asks us to simplify. a[bcos(C)-c.cos(B)]. ......................(1).

Where a,b,c are sides of any triangle and A,B,C are its angles.

Using a= bcos(C)+c.cos(B). (Projection rule)

The expression (1) simplifies to

=b^2cos^2(C)-c^2cos^2(B)....... (2)

=b^2[1-sin^2(C)]-c^2[1-sin^2(B)]

=b^2-c^2-b^2sin^2(C)+c^2sin^2(B)............(3)

But sine rule says .....

bsin(C)=csin(B)

Implying that

b^2sin^2(C)=c^2sin^2(B)

Hence the expression (3) simplifies to

=b^2-c^2........ (4)

So far so good but comparing (4) with (2)

We may deduce cos^2(C)=1=cos^2(B)......

Implying C=B=90 degrees !!!!! .....( not a triangle!!)

Are you kidding ALGEBRA !!!!

Note by Abhinav Raichur
4 years, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$