Some Trigonometry Formulas For Class 10, 11 , 12 in Hindi

Trigonometry: Formulas

" Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. "

Trigonometry Ratios ( त्रिकोणमितीय अनुपात )

त्रिकोणमितीय अनुपात एक समकोण त्रिभुज के किनारों के बीच का अनुपात है।
" Trigonometric ratios are the ratios between edges of a right triangle. "
  1. sinθ =  perpendicular (लंम्ब ) / Hypotenuse (कर्ण)
  2. cosθ = base (आधार) / Hypotenuse (कर्ण)
  3. tanθ = perpendicular (लंम्ब ) / base (आधार)
  4. cosecθ =  Hypotenuse (कर्ण) / perpendicular (लंम्ब )
  5. secθ = Hypotenuse (कर्ण) / base (आधार)
  6. cotθ = base (आधार) / perpendicular (लंम्ब )

Trigonometric Ratio of Certain Angles (कोणों के त्रिकोणमितीय अनुपात)

Angles  ⇒30°45°60°90°
Radians  ⇒0π/6π/4π/3π/2
Sin θ01/21/√2√3/21
Cos θ1√3/21/√21/20
Tan θ01/√31√3
Cot θ√311/√30
Sec θ12/√3√22
Cosec θ2√22/√31

 

Important Formula for Sum and Difference Of Two Angles  :

  1. Sin (A+B) = Sin A Cos B + Cos A Sin B
  2. Sin (A-B) = Sin A Cos B – Cos A Sin B
  3. Cos (A+B) = Cos A Cos B – Sin A Sin B
  4. Cos (A-B) = Cos A Cos B + Sin A Sin B
  5. 2 sinA.cosB = sin(A+B)+sin (A-B)
  6. 2 cosA.sinB = sin(A+B)-sin (A-B)
  7.  2 sinA.sinB = cos(A-B)-cos(A+B)
  8.  2 cosA.cosB = cos(A+B)+cos(A-B)

Transformation of products and Sum :

Sin A Sin B = ½ [Cos (A-B) – Cos (A+B)]

Cos A Cos B = ½ [Cos (A-B) + Cos (A+B)]

Sin A Cos B = ½ [Sin (A+B) + Sin (A-B)]

Cos A Sin B = ½ [Sin (A+B) – Sin (A-B)]

Sin A + Sin B = 2 sin [(A+B )/2 ] cos [(AB) /2]

Sin A – Sin B = 2 cos[(A+B) /2] sin [(AB)/2]

Cos A + Cos B = 2 cos [(A+B )/2 ] cos [(AB) / 2]

Cos A – Cos B = – 2 sin[(A+B) /2] sin [(AB) /2]

Different Formula For Tangent :

  1. tan(A+B) = [(tan tan B)/(– tan tan B)]
  2. tan(A-B) = [(tan A – tan B)/(1 + tan tan B)]
  3. cot(A+B= [(coco− 1)/(cocoA)]
  4. cot(A-B= [(cocoB + 1)/(coB – coA)]

Sign of Trigonometric Functions in Different Quadrants :

Quadrants ⇒IIIIIIIV
Sin A++
Cos A++
Tan A++
Cot A ++
Sec A++
Cosec A ++