Home
Class 12
MATHS
In triangle ABC, if cosA+sinA-(2)/(cosB+...

In `triangle ABC`, if `cosA+sinA-(2)/(cosB+sinB)=0` then prove that triangle is isosceles right angled.

Text Solution

Verified by Experts

Given `(cosA+sinA)(cosB+sinB)=2`
`rArrcos(A-B)+sin(A+B)=2`
`rArr cos(A-B)=1,sin(A+B)=1`
`rArr A=B,A+B=(pi)/(2)`
`rArr C=(pi)/(2)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.2|7 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.3|13 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

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

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

In triangleABC , if cosA=sinB-cosC , then the triangle is

In triangle ABC, 2(bc cosA-ac cosB-ab cosC)=

If a cos A = b cos B , prove that the Delta ABC is either isosceles or right angled.

If in triangle ABC, cosA=(sinB)/(2sinC) , then the triangle is

"In a "DeltaABC, if(cosA)/a=(cosB)/b,"show that the triangle is isosceles".

In any triangle ABC if 2cos B=(a)/(c), then the triangle is(A) Right angled (C) Isosceles (B) Equilateral (D) None of these

If in a triangle ABC, (cosA)/a=(cosB)/b=(cosC)/c ,then the triangle is

triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) . Prove that triangle ABC is a right triangle.

In a triangle ABC cosA+cosB+cosC<=k then k=