Advertisements
Advertisements
Question
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Advertisements
Solution
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
⇒ `(sin(90^circ - 41^circ)/sin41^circ)^2 + (cos(90^circ - 49^circ)/sin49^circ)^2`
⇒ `(cos41^circ/sin41^circ)^2 + (sin49^circ/sin49^circ)^2`
⇒ 1 + 1 = 2
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`sin theta/((cot theta + "cosec" theta)) - sin theta/((cot theta - "cosec" theta)) = 2`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
Prove the following identity :
`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Evaluate:
`(tan 65°)/(cot 25°)`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `(cot A + "cosec" A - 1)/(cot A - "cosec" A + 1) = (1 + cos A)/(sin A)`.
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
