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If 10sin^4alpha+15cos^4alpha=6 , find th...

If `10sin^4alpha+15cos^4alpha=6` , find the value of `27cos e c^6alpha+8s e c^6alpha` .

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To solve the problem, we need to find the value of \( 27 \cos^6 \alpha + 8 \sin^6 \alpha \) given that \( 10 \sin^4 \alpha + 15 \cos^4 \alpha = 6 \). ### Step 1: Rewrite the given equation We start with the equation: \[ 10 \sin^4 \alpha + 15 \cos^4 \alpha = 6 \] ...
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RD SHARMA-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Find sintheta + t a nthetaifcostheta=-(12)/(13)a n d theta lies i...

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  2. If (sinA)/(sinB)=pa n d(cosA)/(cosB)=q , find tanAa n dtanBdot

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  3. If 10sin^4alpha+15cos^4alpha=6 , find the value of 27cos e c^6alpha+8s...

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  4. If a=s e ctheta-t a ntheta and b=cos e ctheta+cottheta , then show tha...

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  5. If cotx(1+sinx)=4m andcotx(1-sinx)=4n , prove that (m^2-n^2)^2=m n .

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  6. If Tn=sin^nx+cos^nx , prove that (i) 2T6-3T4+10=0

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  7. Prove that: sqrt((1-sintheta)/(1+sin theta))+sqrt((1+sintheta)/(1-sint...

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  8. If sectheta+tantheta=p , obtain the values of sectheta,tantheta and s...

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  9. If acos theta-b sin theta=c , show that asin theta+b cos theta=+-sqrt(...

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  10. If t a ntheta+sintheta=m and tantheta-sintheta=n , show m^(2-)n^2=4sq...

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  11. Prove that: s e c^2theta+cos e c^2theta=cosec^2θ.sec^2θ .

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  12. Given that: (1+cosalpha)(1+cosbeta)(1+cosgamma)=(1-cosalpha)(1-cosbeta...

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  13. Prove that: 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta...

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  14. Prove that: 2s e c^2theta-s e c^4theta-2cos e c^2theta+cos e c^4theta=...

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  15. If A lies in second quadrant and 3tanA+4=0, then the value of 2cotA-5c...

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  16. Which of the following is correct? s in1^0> s in1 (b) s in1^0<s in1 ...

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  17. If f(x)=cos^2x+s e c^2x ,t h e n (a)f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1...

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  18. If sectheta=x+1/(4x), then s e ctheta+t a ntheta= (a)x ,1/x (b) 2x ,...

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  19. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if x+y!=0 (b) x=...

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  20. If cos e cx+cotx=(11)/2 , then t a nx= (a)(21)/(22) (b) (15)/(16) (...

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