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प्रश्न
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
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उत्तर
We have,
`sin^2 θ+1/(1+tan^2θ)= sin^2θ+1/(sqc^2θ)`
=` sin^2θ+(1/secθ)^2`
=` sin^2 θ+cos^2θ`
=` 1`
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संबंधित प्रश्न
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ...[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square ...`[cos theta = 1/sectheta]`
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
Prove that `(sec A)/(tan A + cot A) = sin A`.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
