(D) Given,$\cos A \cos B + \sin A \sin B \sin C = 1$ and $C = \frac{\pi}{2}$.Since $C = \frac{\pi}{2}$,we have $\sin C = \sin \frac{\pi}{2} = 1$.Subst

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Given,$\cos A \cos B + \sin A \sin B \sin C = 1$ and $C = \frac{\pi}{2}$.Since $C = \frac{\pi}{2}$,we have $\sin C = \sin \frac{\pi}{2} = 1$.Substituting this into the equation,we get $\cos A \cos B + \sin A \sin B = 1$.Using the trigonometric identity $\cos(A - B) = \cos A \cos B + \sin A \sin B$,the equation becomes $\cos(A - B) = 1$.This implies $A - B = 0$,which means $A = B$.Therefore,the ratio $A : B = 1 : 1$.

Class 11 Mathematics Trigonometrical Equations Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

Easy

In $\triangle ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$ and $C = \frac{\pi}{2}$,then $A : B =$

TS EAMCET 2018 All TS EAMCET

A
$1 : 4$
B
$1 : 3$
C
$1 : 2$
D
$1 : 1$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

Previous Year

TS EAMCET 2018 Paper All TS EAMCET years →

$ABCD$ is a rhombus. The circumradii of $\Delta ABD$ and $\Delta ACD$ are $\frac{25}{2}$ and $25$ respectively. Then the area of the rhombus is .............. $sq. \, unit$.

View Solution

In triangle $ABC$,if $A=45^{\circ}$,$C=75^{\circ}$ and $R=\sqrt{2}$,then $r=$

MediumTS EAMCET 2024

View Solution

In a $\triangle ABC$,$(b^2-c^2) \cot A + (c^2-a^2) \cot B =$

DifficultTS EAMCET 2020

View Solution

In $\triangle ABC$,if $A = 60^{\circ}$ and $B = 105^{\circ}$,then find the value of $\frac{2R^2(b-c) \sin A \sin B \sin C}{(b+c)(s-a \cos C - c \cos A)(s-a \cos B - b \cos A)}$.

DifficultAP EAMCET 2018

View Solution

If the equation $\sin^4 x - (p+2) \sin^2 x - (p+3) = 0$ has a solution, then $p$ must lie in the interval:

MediumWBJEE 2025

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In $\triangle ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$ and $C = \frac{\pi}{2}$,then $A : B =$

Similar Questions

$ABCD$ is a rhombus. The circumradii of $\Delta ABD$ and $\Delta ACD$ are $\frac{25}{2}$ and $25$ respectively. Then the area of the rhombus is .............. $sq. \, unit$.

In triangle $ABC$,if $A=45^{\circ}$,$C=75^{\circ}$ and $R=\sqrt{2}$,then $r=$

In a $\triangle ABC$,$(b^2-c^2) \cot A + (c^2-a^2) \cot B =$

In $\triangle ABC$,if $A = 60^{\circ}$ and $B = 105^{\circ}$,then find the value of $\frac{2R^2(b-c) \sin A \sin B \sin C}{(b+c)(s-a \cos C - c \cos A)(s-a \cos B - b \cos A)}$.

If the equation $\sin^4 x - (p+2) \sin^2 x - (p+3) = 0$ has a solution, then $p$ must lie in the interval:

Vedclass Test Series

Exam Paper Generator

Online Exam Module