Amit classes
Class – 10th
Assignment ( trigonometry)
𝑆𝑖𝑛𝐴−2𝑆𝑖𝑛3 𝐴
Q.1 Prove that: = tan 𝐴 (𝜃 𝑖𝑠 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑑 𝑏𝑦 𝐴)
2𝑐𝑜𝑠3 𝐴−cos 𝐴
𝑐𝑜𝑡 2 𝛼
Q.2 Prove that 1 + = 𝑐𝑜𝑠𝑒𝑐 𝛼
1+𝑐𝑜𝑠𝑒𝑐 𝛼
Q.3 Prove that: (𝑠𝑖𝑛𝜃 + 1 + 𝑐𝑜𝑠𝜃 )(𝑠𝑖𝑛𝜃 − 1 + 𝑐𝑜𝑠𝜃 ). 𝑠𝑒𝑐𝜃𝑐𝑜𝑠𝑒𝑐𝜃
=2
1 1
Q.4 if 𝑠𝑒𝑐𝜃 = 𝑥 + , prove that 𝑠𝑒𝑐𝜃 + tan 𝜃 = 2𝑥 𝑜𝑟 .
4𝑥 2𝑥
1
Q.5 if 1 + 𝑠𝑖𝑛3 𝜃 = 3 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃, 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 𝑡𝑎𝑛𝜃 = 1 𝑜𝑟 .
2
Q.6 if 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠𝜃, 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 2 𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑠 2 𝜃.
1−𝑠𝑖𝑛𝜃
Q.7 Prove that : = (𝑠𝑒𝑐𝜃 − 𝑡𝑎𝑛𝜃)2 .
1+sin 𝜃
𝑐𝑜𝑠𝜃−𝑠𝑖𝑛𝜃 1−√3
Q.8 Find an acute angle𝜃, when = .
𝑐𝑜𝑠𝜃+𝑠𝑖𝑛𝜃 1+√3
𝑐𝑜𝑠3 𝜃+𝑠𝑖𝑛3 𝜃 𝑐𝑜𝑠3 𝜃−𝑠𝑖𝑛3 𝜃
Q.9 Prove that: + =2
𝑐𝑜𝑠𝜃+𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃−𝑠𝑖𝑛𝜃
Q.10 If 𝑥 𝑠𝑖𝑛3 𝜃 + 𝑦𝑐𝑜𝑠 3 𝜃 = 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃 𝑎𝑛𝑑 𝑥 sin 𝜃 = 𝑦𝑐𝑜𝑠𝜃, prove
𝑥 2 + 𝑦2 = 1
Q.11 If tan𝜃 + sin 𝜃 = 𝑚 𝑎𝑛𝑑 𝑡𝑎𝑛𝜃 − 𝑠𝑖𝑛𝜃 = 𝑛, show that (𝑚2 −
𝑛2 ) = 4√𝑚𝑛.
Q.12If sin 𝜃 = 𝑐𝑜𝑠𝜃, 𝑡ℎ𝑒𝑛 find the value of 2 tan𝜃 + 𝑐𝑜𝑠 2 𝜃.
Q.13 if 𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃 = √3, then prove that 𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑡𝜃 = 1.
Class – 10th
Assignment ( trigonometry)
𝑆𝑖𝑛𝐴−2𝑆𝑖𝑛3 𝐴
Q.1 Prove that: = tan 𝐴 (𝜃 𝑖𝑠 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑑 𝑏𝑦 𝐴)
2𝑐𝑜𝑠3 𝐴−cos 𝐴
𝑐𝑜𝑡 2 𝛼
Q.2 Prove that 1 + = 𝑐𝑜𝑠𝑒𝑐 𝛼
1+𝑐𝑜𝑠𝑒𝑐 𝛼
Q.3 Prove that: (𝑠𝑖𝑛𝜃 + 1 + 𝑐𝑜𝑠𝜃 )(𝑠𝑖𝑛𝜃 − 1 + 𝑐𝑜𝑠𝜃 ). 𝑠𝑒𝑐𝜃𝑐𝑜𝑠𝑒𝑐𝜃
=2
1 1
Q.4 if 𝑠𝑒𝑐𝜃 = 𝑥 + , prove that 𝑠𝑒𝑐𝜃 + tan 𝜃 = 2𝑥 𝑜𝑟 .
4𝑥 2𝑥
1
Q.5 if 1 + 𝑠𝑖𝑛3 𝜃 = 3 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃, 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡 𝑡𝑎𝑛𝜃 = 1 𝑜𝑟 .
2
Q.6 if 𝑠𝑖𝑛𝜃 = 𝑐𝑜𝑠𝜃, 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 2 𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑠 2 𝜃.
1−𝑠𝑖𝑛𝜃
Q.7 Prove that : = (𝑠𝑒𝑐𝜃 − 𝑡𝑎𝑛𝜃)2 .
1+sin 𝜃
𝑐𝑜𝑠𝜃−𝑠𝑖𝑛𝜃 1−√3
Q.8 Find an acute angle𝜃, when = .
𝑐𝑜𝑠𝜃+𝑠𝑖𝑛𝜃 1+√3
𝑐𝑜𝑠3 𝜃+𝑠𝑖𝑛3 𝜃 𝑐𝑜𝑠3 𝜃−𝑠𝑖𝑛3 𝜃
Q.9 Prove that: + =2
𝑐𝑜𝑠𝜃+𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃−𝑠𝑖𝑛𝜃
Q.10 If 𝑥 𝑠𝑖𝑛3 𝜃 + 𝑦𝑐𝑜𝑠 3 𝜃 = 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃 𝑎𝑛𝑑 𝑥 sin 𝜃 = 𝑦𝑐𝑜𝑠𝜃, prove
𝑥 2 + 𝑦2 = 1
Q.11 If tan𝜃 + sin 𝜃 = 𝑚 𝑎𝑛𝑑 𝑡𝑎𝑛𝜃 − 𝑠𝑖𝑛𝜃 = 𝑛, show that (𝑚2 −
𝑛2 ) = 4√𝑚𝑛.
Q.12If sin 𝜃 = 𝑐𝑜𝑠𝜃, 𝑡ℎ𝑒𝑛 find the value of 2 tan𝜃 + 𝑐𝑜𝑠 2 𝜃.
Q.13 if 𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃 = √3, then prove that 𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑡𝜃 = 1.
