Advertisements
Advertisements
Question
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Solution
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Consider `sec70^circ sin20^circ - cos20^circ cosec70^circ`
⇒ `sec(90^circ - 20^circ)sin20^circ - cos20^circ . cosec(90^circ - 20^circ)`
⇒ `cosec20^circ sin20^circ - cos20^circ sec20^circ`
⇒ `1/sin20^circ . sin20^circ - cos20^circ . 1/cos20^circ`
⇒ 1 - 1 = 0
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
`1+(tan^2 theta)/((1+ sec theta))= sec theta`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Find the value of ( sin2 33° + sin2 57°).
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or `1/2`.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
