Question

please write all the formulas of trigonomety class 10

Answer 1

SOME FORMULAE OF TRIGONOMETRY OF CLASS 10 AS THE FOLLOWING:

There are some properties pertaining to the right-angled triangle. It is to be noted that in the following formulas, P stands for perpendicular, B stands for base and H stands for the hypotenuse.

SinA = P / H

CosA = B / H

TanA = P / B

CotA = B / P

CosecA = H / P

SecA = H/B

Sin2A + Cos2A = 1

Tan2A + 1 = Sec2A

Cot2A + 1 = Cosec2A

In order to find a relationship between various trigonometric identities, there are some important formulas:

1. TanA = SinA / CosA

2. CotA = CosA / SinA

3. CosecA = 1 / SinA

4. SecA = 1 / CosA

There are some formulas that are very crucial to solving higher level sums.

Sin (A +B) =SinA . CosB + CosA . SinB

Sin (A – B) = SinA . CosB – CosA . SinB

Cos (A + B) = CosA . CosB – SinA . SinB

Cos (A – B) = CosA. CosB + SinA . SinB

Tan (A + B) = TanA + TanB / 1 – TanA . TanB

Tan (A – B) = TanA –TanB / 1 + TanA . TanB

Sin ( A + B) . Sin (A – B) = Sin2A – Sin2B = Cos2B – Cos2A

Cos (A + B) . Cos (A – B) = Cos2A – Sin2B = Cos2B – Sin2A

Sin2A = 2 . SinA . CosA = 2 . TanA / (1 + Tan2A)

Cos2A = Cos2A – Sin2A = 1 – 2Sin2A = 2Cos2A – 1 = (1 – Tan2A) / (1 + Tan2A)

Tan2A = 2TanA / (1 – Tan2A)

 Sin3A = 3 . SinA – 4 . Sin3A

Cos3A = 4 . Cos3A – 3 . CosA

Tan3A = (3TanA – Tan3A) / (1 – 3Tan2A)

SinA + SinB = 2 Sin (A + B)/2 Cos (A – B)/2

SinA – SinB = 2 Sin (A – B)/2 Cos (A + B)/2

CosA + CosB = 2 Cos(A – B)/2 Cos (A + B)/2

CosA – CosB = 2 Sin(B – A)/2 Sin (A + B)/2

TanA + TanB = Sin (A + B) / CosA . CosB

SinA CosB = Sin (A + B) + Sin (A – B)

CosA SinB = Sin (A + B) – Sin (A – B)

CosA CosB = Cos (A + B) + Cos (A – B)

 SinA SinB = Cos (A – B) – Cos (A + B)

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Answer 2

$cosec \: o \: = \: \frac{1}{ \sin \: o } \\ \\ sec \: o = \frac{1}{ \cos \: o } \\ \\ cot \: o \: = \frac{1}{tan \: o} \\ \\ sin \: o \: = \: cos \: (90 - o) \\ \\ \frac{sin \: o}{cos \: o} = 1 \\ \\ cos \: o = sin \: (90 - o) \\ \\ tan \: o \: \times tan(90 - o) = 1$