Question

from the following figure find the values of
1.Cos a
2.Cosec a
3.tan²a - sec²a
4.sin c
5.sec c
6.cot²C - 1/Sin²C
​

Answer 1

Step-by-step explanation:

1)cosa=adjacent side/hypotenuse=3/5.

2) cosec a=hypotenuse/opposite side =5/4

3)tan^2a-sec^2a=(opposite side/adjacent side)^2-(hypo./adjacent side)^2

tan^2a-sec^2a=(4/3)^2-(5/3)^2=(16-25)/9= -9/9= -1

tan^2a-sec^2a= -1

4)sin c=opposite /hypo.=4/12=1/3

5)sec c=hypo./adjacent side=12/10=6/5

6)cot^2c-1/sin^2c=(adjacent side/opposite side)^2-1/(opposite side/hypo.)^2

cot^2c-1/sin^2c=(10/4)^2-(hypo./opposite side)^2

cot^2c-1/sin^2c=100/16-(12/4)^2.

cot^2c-1/sin^2c=100/16-144/16=(100-144)/16=-44/16

cot^2c-1/sin^2c= -11/4