Textbook Solutions: Trigonometry | Mathematics Class 10 (Maharashtra SSC Board) PDF Download

 Page 1


Trigonometry 
Practice Set 6.1 
Q. 1. If Sin?? = 
?? ????
, find the values of cos? and tan?. 
Answer : We know that, 
 
sin
2
? + cos
2
? = 1 
 
 
 
 
 
Also, 
 
 
Q. 2. If tan?? = 
?? ?? , find the values of sec? and cos?. 
Answer : We know that, 
 
sec
2
?= 1 + tan
2
? 
 
Page 2


Trigonometry 
Practice Set 6.1 
Q. 1. If Sin?? = 
?? ????
, find the values of cos? and tan?. 
Answer : We know that, 
 
sin
2
? + cos
2
? = 1 
 
 
 
 
 
Also, 
 
 
Q. 2. If tan?? = 
?? ?? , find the values of sec? and cos?. 
Answer : We know that, 
 
sec
2
?= 1 + tan
2
? 
 
 
 
 
 
Also, 
 
 
Q. 3. If cot?? = 
????
?? , find the values of cosec? and sin?. 
Answer : We know that, 
cosec
2
? = 1 + cot
2
? 
 
 
 
?      
Also, 
 
Page 3


Trigonometry 
Practice Set 6.1 
Q. 1. If Sin?? = 
?? ????
, find the values of cos? and tan?. 
Answer : We know that, 
 
sin
2
? + cos
2
? = 1 
 
 
 
 
 
Also, 
 
 
Q. 2. If tan?? = 
?? ?? , find the values of sec? and cos?. 
Answer : We know that, 
 
sec
2
?= 1 + tan
2
? 
 
 
 
 
 
Also, 
 
 
Q. 3. If cot?? = 
????
?? , find the values of cosec? and sin?. 
Answer : We know that, 
cosec
2
? = 1 + cot
2
? 
 
 
 
?      
Also, 
 
Q. 4. If 5sec?- 12cosec? = 0, find the values of sec?, cos? and sin?. 
Answer : 5sec? - 12cosec? = 0 
 
? 5sec? = 12cosec? 
 
 
 
As  we have, 
 
Also, We know that, 
sec
2
?= 1 + tan
2
? 
 
 
 
 
Also, 
 
Page 4


Trigonometry 
Practice Set 6.1 
Q. 1. If Sin?? = 
?? ????
, find the values of cos? and tan?. 
Answer : We know that, 
 
sin
2
? + cos
2
? = 1 
 
 
 
 
 
Also, 
 
 
Q. 2. If tan?? = 
?? ?? , find the values of sec? and cos?. 
Answer : We know that, 
 
sec
2
?= 1 + tan
2
? 
 
 
 
 
 
Also, 
 
 
Q. 3. If cot?? = 
????
?? , find the values of cosec? and sin?. 
Answer : We know that, 
cosec
2
? = 1 + cot
2
? 
 
 
 
?      
Also, 
 
Q. 4. If 5sec?- 12cosec? = 0, find the values of sec?, cos? and sin?. 
Answer : 5sec? - 12cosec? = 0 
 
? 5sec? = 12cosec? 
 
 
 
As  we have, 
 
Also, We know that, 
sec
2
?= 1 + tan
2
? 
 
 
 
 
Also, 
 
 
Now, again using 
 
 
 
 
Q. 5. If tan? = 1 then, find the values of  
Answer : Given, 
tan ? = 1 
? ? = 45° [as tan 45° = 1] 
Also, 
 
 
 
 
= sin? cos? 
Page 5


Trigonometry 
Practice Set 6.1 
Q. 1. If Sin?? = 
?? ????
, find the values of cos? and tan?. 
Answer : We know that, 
 
sin
2
? + cos
2
? = 1 
 
 
 
 
 
Also, 
 
 
Q. 2. If tan?? = 
?? ?? , find the values of sec? and cos?. 
Answer : We know that, 
 
sec
2
?= 1 + tan
2
? 
 
 
 
 
 
Also, 
 
 
Q. 3. If cot?? = 
????
?? , find the values of cosec? and sin?. 
Answer : We know that, 
cosec
2
? = 1 + cot
2
? 
 
 
 
?      
Also, 
 
Q. 4. If 5sec?- 12cosec? = 0, find the values of sec?, cos? and sin?. 
Answer : 5sec? - 12cosec? = 0 
 
? 5sec? = 12cosec? 
 
 
 
As  we have, 
 
Also, We know that, 
sec
2
?= 1 + tan
2
? 
 
 
 
 
Also, 
 
 
Now, again using 
 
 
 
 
Q. 5. If tan? = 1 then, find the values of  
Answer : Given, 
tan ? = 1 
? ? = 45° [as tan 45° = 1] 
Also, 
 
 
 
 
= sin? cos? 
= sin 45° cos 45° 
 
Q. 1. A. Prove that: 
 
 
Answer : Taking LHS 
 
 
 [As, sin
2
? + cos
2
? = 1] 
= sec ?  
= RHS 
Proved ! 
Q. 6. B. Prove that: 
 
 
Answer : Taking LHS 
cos
2
?(1 + tan
2
?) 
= cos
2
? sec
2
? [As, sec
2
? = 1 + tan
2
?] 
 
= 1