Paragraph: Read the following information and answer Let t_n= ^n θ+ ^n θ . Question: What is the value of t_ 10 where θ=45^ ^ ?

Correct answer: C. (1)/(16) t_ 10 = ^ 10 (θ)+ ^ 10 (θ) When θ=45^ ^ , t_ 10 = ^ 10 (45^ ^ )+ ^ 10 (45^ ^ ) aligned & =( 1 2 )^ 10 +( 1 2 )^ 10 =2 ·( 1 2 )^ 10 & =2 × (1)/(32)=(1)/(16) aligned

NDA 2020

Exam: NDA
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2020 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Read the following information and answer Let t_n= ^n θ+...

Paragraph: Read the following information and answer Let

t_n=\sin ^n \theta+\cos ^n \theta

.
Question: What is the value of

t_{10}

where

\theta=45^{{}^{\circ}}

Options

A1
B $\frac{1}{4}$
C $\frac{1}{16}$
D $\frac{1}{32}$

Correct answer

C. $\frac{1}{16}$

Step-by-step solution

t_{10}=\sin ^{10}(\theta)+\cos ^{10}(\theta)

When

\theta=45^{{}^{\circ}}

t_{10}=\sin ^{10}\left(45^{{}^{\circ}}\right)+\cos ^{10}\left(45^{{}^{\circ}}\right)

\begin{aligned} & =\left(\frac{1}{\sqrt{2}}\right)^{10}+\left(\frac{1}{\sqrt{2}}\right)^{10}=2 \cdot\left(\frac{1}{\sqrt{2}}\right)^{10} \\ & =2 \times \frac{1}{32}=\frac{1}{16}\end{aligned}

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