Aptitude - Trigonometry
2.
sin (50° + θ) − cos (40° − θ) = ?
Answer
sin (50° + θ) − cos (40° − θ)
= sin [90° − (40° − θ)] − cos (40° − θ)
= cos (40° − θ) − cos (40° − θ) = 0
Answer :
Option AExplanation :
sin (50° + θ) − cos (40° − θ)
= sin [90° − (40° − θ)] − cos (40° − θ)
= cos (40° − θ) − cos (40° − θ) = 0
3.
If (tan θ + cot θ) = 5, then (tan2 θ + cot2 θ) = ?
Answer
(tan θ + cot θ) = 5 ⇒ (tan θ + cot θ)2 = 25
⇒ tan2θ + cot2θ + 2tan θ cot θ = 25
⇒ tan2θ + cot2θ + 2 = 25
⇒ tan2θ + cot2θ = 25 − 2 = 23
Answer :
Option CExplanation :
(tan θ + cot θ) = 5 ⇒ (tan θ + cot θ)2 = 25
⇒ tan2θ + cot2θ + 2tan θ cot θ = 25
⇒ tan2θ + cot2θ + 2 = 25
⇒ tan2θ + cot2θ = 25 − 2 = 23
4.
sin 60° cos 30° + cos 60° sin 30° = ?
Answer
sin 60° cos 30° + cos 60° sin 30° = √32 x √32 + 12 x 12 = 34 + 14 = 44 = 1
Answer :
Option CExplanation :
sin 60° cos 30° + cos 60° sin 30° = √32 x √32 + 12 x 12 = 34 + 14 = 44 = 1
5.
If xtan 45° cos 60° = sin 60° cot 60°, then x = ?
Answer
xtan 45° cos 60° = sin 60° cot 60°
⇒ x x 1 x 12 = √32 x 1√3 ⇒ x = 1
Answer :
Option BExplanation :
xtan 45° cos 60° = sin 60° cot 60°
⇒ x x 1 x 12 = √32 x 1√3 ⇒ x = 1
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