Home
Class 12
MATHS
If alpha and beta are acute angles such ...

If `alpha` and `beta` are acute angles such that `alpha+beta=lamda`, where constant, find the maximum possible value of the expression `sin alpha+sin beta+cos alpha+cos beta`.

Text Solution

AI Generated Solution

To find the maximum possible value of the expression \( \sin \alpha + \sin \beta + \cos \alpha + \cos \beta \) given that \( \alpha + \beta = \lambda \), we can follow these steps: ### Step 1: Rewrite the Expression We start with the expression: \[ y = \sin \alpha + \sin \beta + \cos \alpha + \cos \beta \] ...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Solved example|15 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.1|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If sin beta is the GM between sin alpha and cos alpha, then cos 2beta=

Let alpha, beta, gamma be the measures of angle such that sin alpha+sin beta+sin gamma ge 2 . Then the possible value of cos alpha + cos beta+cos gamma is

If alpha and beta are acute angles and sin alpha = (3)/(5) , sin beta = (8)/( 17), find the values of sin ( alpha + beta), cos (alpha pm beta), and tan ( alpha pm beta).

alpha, beta, gamma are real number satisfying alpha+beta+gamma=pi . The minimum value of the given expression sin alpha+sin beta+sin gamma is

alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2beta) then tan alpha cot beta =

If sin alpha cos beta=-(1)/(2) then find the range of values of cos alpha sin beta

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If alpha+gamma=2beta then the expression (sin alpha-sin gamma)/(cos gamma-cos alpha) simplifies to:

A vector makes angles alpha,beta "and" gamma with the X,Y and Z axes respectively . Find the value of the expression (sin^(2)alpha+sin^(2)beta+sin^(2)gamma)/(cos^(2)alpha+cos^(2)beta+cos^(2)gamma)

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|