If sin theta + cos theta = p and sin^3 theta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given,$\sin 	heta + \cos 	heta = p$  $(i)$ and $\sin^3 	heta + \cos^3 	heta = q$  $(ii)$ We know that $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. S

Vedclass · Accepted Answer

$-2q$

Vedclass · Answer

(D) Given,$\sin 	heta + \cos 	heta = p$  $(i)$ and $\sin^3 	heta + \cos^3 	heta = q$  $(ii)$ We know that $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. So,$(\sin 	heta + \cos 	heta)(\sin^2 	heta - \sin 	heta \cos 	heta + \cos^2 	heta) = q$ $p(1 - \sin 	heta \cos 	heta) = q$  (since $\sin^2 	heta + \cos^2 	heta = 1$) $1 - \sin 	heta \cos 	heta = \frac{q}{p}$ $\sin 	heta \cos 	heta = 1 - \frac{q}{p} = \frac{p - q}{p}$  $(iii)$ Now,square equation $(i)$: $(\sin 	heta + \cos 	heta)^2 = p^2$ $\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta = p^2$ $1 + 2 \sin 	heta \cos 	heta = p^2$ Substitute $\sin 	heta \cos 	heta$ from $(iii)$: $1 + 2 \left( \frac{p - q}{p} ight) = p^2$ $p + 2p - 2q = p^3$ $3p - 2q = p^3$ $p^3 - 3p = -2q$ $p(p^2 - 3) = -2q$

If $\sin \theta + \cos \theta = p$ and $\sin^3 \theta + \cos^3 \theta = q$,then $p(p^2 - 3)$ is equal to

Similar Questions

The relative reactivities of acyl compounds towards nucleophilic substitution are in the order of

Which of the following ecosystem types has the highest annual net primary productivity?

$A$ paramagnetic sample shows a net magnetization of $8 \ Am^{-1}$ when placed in an external magnetic field of $0.6 \ T$ at a temperature of $4 \ K$. When the same sample is placed in an external magnetic field of $0.2 \ T$ at a temperature of $16 \ K$,the magnetization will be

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is : (in $: 1$)

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module