English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = π2 - Mathematics

Advertisements
Advertisements

Question

Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`

Sum
Advertisements

Solution

Taking A + B = X and C = Y

We get cos(X + Y) = cos X cos Y – sin X sin Y

(i.e) cos(A + B + C) = cos(A + B) cos C – sin(A + B) sin C

= (cos A cos B – sin A sin B) cos C – [sin A cos B + cos A sin B] sin C

cos(A + B + C) = cos A cos B cos C – sin A sin B cos C – sin A cos B sin C – cos A sin B sin C

If (A + B + C) = `π/2` then cos(A + B + C) = 0

⇒ cos A cos B cos C – sin A sin B cos C – sin A cos B sin C – cos A sin B sin C = 0

⇒ cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin

C sin A cos B

shaalaa.com
Trigonometric Functions and Their Properties
  Is there an error in this question or solution?
Chapter 3: Trigonometry - Exercise 3.4 [Page 109]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 3 Trigonometry
Exercise 3.4 | Q 8 | Page 109

RELATED QUESTIONS

Find the values of sin(480°)


Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ


If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)


If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)


Find the value of cos 105°.


Find a quadratic equation whose roots are sin 15° and cos 15°


If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y


Prove that sin 75° – sin 15° = cos 105° + cos 15°


Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)


If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0


Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`


Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`


Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`


Express the following as a product
cos 65° + cos 15°


Show that sin 12° sin 48° sin 54° = `1/8`


If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C


If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos  "A"/2 cos  "B"/2 cos  "C"/2`


Choose the correct alternative:
`(1 + cos  pi/8) (1 + cos  (3pi)/8) (1 + cos  (5pi)/8) (1 + cos  (7pi)/8)` =


Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×