Question

If cosec (A-20°)=sec 4A where 20°<A and 4A is an acute angle then find the value of A?

Answer 1

Hi , there !!

cosec ( A -20 ° ) = sec4 A

sec 4 A= Cosec ( 90 -4 A )

on equating we get the

Cosec ( A -20 ) = Cosec ( 90 -4 A )

=> A -20° = 90° -4A

=> 5A = 110°


=> 22 °
where A< 90°

hope it helps !!

thanks !!

ranjan kumar

Answer 2

cosec(A-20°) = sec4A

that means

1/sin(A-20°) = 1/cos4A

therefore , sin(A-20°) = cos4A

we know that cosA = sinA when A=45°

4A = 45 , that is , A=45/4= 11.25°

A-20° = 45 , so A= 45+20= 65

here we have 2 solutions, but in the condition above it is given that A is greater than 20° , so the answer is 65°