Straight line formulas for class 10 and 11

 

Sin^-1 x + Cos^-1 x = pi/2

 

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Sin(A+B) = sinAcosB + cosAsinB proof

Angle bisector Theorem

 

Quadrilateral full information

In a right angled triangle, the length of the median on its hypotenuse is half the length of the hypotenuse proof

 

Limit x tends to 0 sinX/x = 1 proof

This proof also called SANDWICH THEOREM 

What is SANDWICH theorem?

In this theorem, if  f(x) ≤ g(x) ≤ h(x) for all numbers, and at some point x = k then we have f(k) = h(k), then g(k) must also be equal to them.

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Angle bisector theory prove tan alpha = c/(a+b)

 

Medians of triangle are concurrent and their point of concurrency is the point of trisect of each other.

Heron’s formula proof

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof) BASIC PROPORTIONALITY THEOREM

Converse of Thales theorem by Similarity

Thales theorem or Basic proportionality theorem (BPT)

First True Mathematician-- Thales

Converse of Thales theorem by Similarity ( BPT ) BASIC THALES THEOREM

Similarity Theorem 1

Similarity SAS theorem

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof)

Similarity SSS theorem

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof)

Converse of Thales theorem by Similarity

Similarity SAS theorem

Similarity Theorem 1

Similarity SAS theorem

Similarity Theorem 1

Similarity SSS theorem

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof)

Similarity Theorem 1

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof)

Similarity SSS theorem

Similarity SAS theorem

Thales theorem or Basic proportionality theorem (BPT)

Converse of Thales theorem ( BPT ) by Contradiction ( Actual Proof) BASIC PROPORTIONALITY THEOREM

Converse of Thales theorem by Similarity ( BPT ) BASIC THALES THEOREM

Similarity SAS theorem

Medians of Triangle divides each other at 2:1 ratio