Get 2 FREE Instant-Explanations on Filo with code FILOAPP

In a ABC, { B } { C } + { B } { C } ^{ 2 }{ A } =1.Then th

Question

In a $△ A BC, cos B cos C + sin B sin C sin^{2} A = 1$ .Then the triangle is

Right-angled isosceles

Isosceles where equal angles are greater than

\frac{π}{4}

Equilateral

None of these

Views: 1,000 students

Found 6 tutors discussing this question

Mia Discussed

In a

△ A BC, cos B cos C + sin B sin C sin^{2} A = 1

.Then the triangle is

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

\Rightarrow

A + B + C = π

∴

A = π - (B + C)

Given,

sin^{2} A = \frac{1 - cos B cos C}{sin B sin C} \leq 1

\Rightarrow cos (B - C) \geq 1

∴ cos (B - C) = 1 = cos 0 ∴ B = C

∴ sin^{2} A = \frac{1 - cos ^{2} B}{sin ^{2} B} = 1 \Rightarrow ∠ A = 90^{0}

∴

Triangle is right-angled isosceles

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	In a $△ A BC, cos B cos C + sin B sin C sin^{2} A = 1$ .Then the triangle is
Answer Type	Text solution:1
Upvotes	150