Q 24 In △PQR; if sec R = 2 sin Q cosec P, then △PQR is A an - Maths - Trigonometric Functions

Question

Q 24 In △ PQR; if sec R = 2 sin Q cosec P, then △ PQR
is
A an isosceles triangle
B an equilateral triangle
C a right-angled triangle
D a right-angled isosceles triangle

Aarushi Mishra · Accepted Answer

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sec R=2 sin Q cosec P1cos R=2 sin Qsin PBy sine rulepsin P=qsin Q=rsin Rsin Qsin P=qpBy cosine rulecos R=p2+q2-r22pq1p2+q2-r22pq=2 qp2pqp2+q2-r2=2 qppp2+q2-r2=1pp2+q2-r2=p2q2=r2q=rHence it is an isosceles triangle

Q.24. In △ PQR; if sec R = 2 sin Q cosec P, then △ PQR is A. an isosceles triangle B. an equilateral triangle C. a right-angled triangle D. a right-angled isosceles triangle

Q.24. In $△$ PQR; if sec R = 2 sin Q cosec P, then $△$ PQR is
A. an isosceles triangle
B. an equilateral triangle
C. a right-angled triangle
D. a right-angled isosceles triangle