Question

1. In the figure ∠ CDB = φ , ∠ ACB = θ

∠ ABC = 90° find the values of

a) sin θ

b) 4 (tan θ - sin φ )

Answer 1

Answer:

In the given figure,

∠C=90  

∘

 

In △ABC,

tan∠ABC=  

B

P

​

=  

BC

AC

​

 

In △CDB,

tan∠DBC=  

B

P

​

=  

BC

CD

​

 

Now,

tan∠DBC

tan∠ABC

​

=  

BC

CD

​

 

BC

AC

​

 

​

 

tan∠DBC

tan∠ABC

​

=  

CD

AC

​

 

tan∠DBC

tan∠ABC

​

=  

CD

2CD

​

 

tan∠DBC

tan∠ABC

​

=2 (D is mid point of AC)

Step-by-step explanation: