Question

Cosx=tanY,coty=tanz,cotz=tanx then sinx=

Answer 1

Step-by-step explanation: cosx=tany   .....(1)

coty=tanz   ......(2)

cotz=tanx   .......(3)

⇒cosxtanzcotz=tanycotytanx from (1),(2) and (3)

⇒cosx×1=1×tanx

⇒cosx=  cos x / sin x

⇒cos^2x= sin x

⇒1−sin^2 x−sinx=0

⇒−sin^2 x−sinx+1=0

⇒sin^2 x+sinx−1=0

⇒sinx=  −1±  √1+4 /2 =  −1±  √5/2

​Now, sin18degree is positive, as 18degree lies in first quadrant.

∴,sin18degree =sinA=    −1±  √5/2

Hence sinx=siny=sinz=sin18degree