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Question

In a ABC, if the sides are a=3,b=5 and c=4, then sinB2+cosB2 is equal to


A

2

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B

3+12

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C

3-12

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D

1

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Solution

The correct option is A

2


Explanation for correct option:

Step 1: Finding squares of side and checking for Pythagoras theorem:

Given a triangle ABC in which sides are a=3,b=5 and c=4

Now applying Pythagoras theorem we get,

b2=a2+c2LHS:=52=25RHS:=32+42=9+16=25

Since, LHS =RHS, the triangle ABC is a right-angled triangle at B.

Hence, B=90°

Step 2: Finding the value of the expression sinB2+cosB2:

sinB2+cosB2=sin450+cos450=12+12=22=2

Therefore, the value of the given expression is equal to 2.

Hence, the correct answer is option (A).


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