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If A,B and C,are the angles of a triangle,show that

tan²A/2+tan²B/2+tan²C/2

1

Represet the folloing families of curves by forming the corresponding diffrential eqations, where a and b are parameters.

1. y²= b(a²-x²)

2.(y-b)²= 4(x-a)

3.xy= ae^x+be^-x+x²

4.y²-2ay+x² =a²

Prove that sin 2

/7+sin 4

/7+sin 8

/7=

7/2 .

p

(-infinity,0)

(

2+1)²,infinity

If A,B,C and D are angles of a quadilateral and sin A/2 sin B/2 sin C/2 sin D/2=1/4,prove that A=B=C=D=

/2

_{[1 ]}

^{[n ]} tan r

tan(r+1)

=cot

tan(n+1)

-n-1

Assume 273K

The standard free energy of formation of ammonia is minus 16.48KJ/mol.What is the value of equilibrium constant(R=8.314J/K/Mol)

Let A,B,C be three angles such that A=

/4 and tanBtanC=p.Find all possible values of p such that A,B,C are the angles of triangle.

If tan

tan

=

a-b/

a+b, prove that (a-bcos2

) (a-bcos2

) is independent of

and

Calculate the maximum value of 1+sin(

/4+

) +2cos(

/4-

) for all real vlues of

Trigonometric Functions.