Question

In ∆ ABC, angle c=90 and angle A and angle B are accute angles l.draw appropriate figure and prove that sin²A+cos²A=1​

Answer 1

Answer:

Given that:

∠C=90

∘

,BC=a,AC=b,CD⊥AB,CD=P

To Prove:

P

2

1

=

a

2

1

+

b

2

1

Solution:

A(ABC)=

2

1

ab=

2

1

P×AB

or, AB=

P

ab

In right angled △ACB,

By Pythagorean theorem,

AB

2

=BC

2

+AC

2

or, (

P

ab

)

2

=a

2

+b

2

or,

P

2

a

2

b

2

=a

2

+b

2

Dividing both sides by a

2

b

2

we get,

or,

P

2

1

=

a

2

1

+

b

2

1

Hence, proved.

Answer 2

Answer:

Given that:

∠C=90∘,BC=a,AC=b,CD⊥AB,CD=P

To Prove:

P21=a21+b21

Solution:

A(ABC)=21ab=21P×AB

or, AB=Pab

In right angled △ACB,

By Pythagorean theorem,

AB2=BC2+AC2

or, (Pab)2=a2+b2

or, P2a2b2=a2+b2

Dividing both sides by a2b2 we get,

or, P21=a21+

Step-by-step explanation:

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